development of fuzzy logic architec- ture to assess the

Development of Fuzzy Logic Architec-ture to assess the sustainability of the

Forest Management

C. Jeganathan March 2003

Development of Fuzzy Logic Architecture to Assess Sustainability of Forest Management

By

C. Jeganathan

Thesis submitted to the International Institute for Geo-information Science and Earth Obser-vation in partial fulfilment of the requirements for the degree of Master of Science in Geoin-formatics Degree Assessment Board Chairman: Prof. Dr. Alfred Stein External examiner: Prof. F.A. Lootsma , Delft University of Technology, Delft. Supervisor: Dr. Theo Bouloucos Supervisor: Dr. M.A. Sharifi

INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION

ENSCHEDE, THE NETHERLANDS

Disclaimer This document describes work undertaken as part of a programme of study at the In-ternational Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not nec-essarily represent those of the institute.

DEVELOPMENT OF FUZZY LOGIC ARCHITECTURE TO ASSESS SUSTAINABILITY OF FOREST MANAGEMENT

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ACKNOWLEDGEMENT My sincere thanks to Dr. K. Kasturi Rangan, Chairman, Department of Space, Bangalore, Dr. R. R. Navalgund, Director, National Remote Sensing Agency (NRSA), Hyderabad, Dr. P.S. Roy, Dean, Indian Institute of Remote Sensing (IIRS) and Mr. P.L.N. Raju, In-Charge, Geoinformatics Division, IIRS, Dehradun, India, for recommending me to undergo Masters programme at ITC, Enschede, Netherlands and their kind support. I have deep gratitude to Dr. Ali Sharifi, my supervisor for his kind advice, support in orient-ing me in the direction of decision science and giving his views on the subject in moving my thesis in the right direction. His warmth and lovely discussions will remain memorable al-ways. I am very grateful to him for his affection and availability at all time whenever I needed him. I am also very thankful to supervisor Dr. Theo Bouloucos for his fatherly advice on my work and his critical view on the structure of any matter, which I discuss with him. His enthu-siastic discussions, kind help and support was encouraging during my research period. My truthful thanks to many researchers who have provided their original materials without second thought, to say a few Dr. Luc Aurelien Andriantiatsaholiniaina, Greece ; Prof. F.A. Lootsma, Netherlands and Prof. L. Martinez, Spain. I am also greatful to all the staffs of Eco-label Institute of Indonesia (LEI) for their kind courtesy, especially to Mr. Alan, Mr. Irwin, Mr. Iman & Mr. Anas who have helped in providing all necessary materials during my visit. I am also thankful to experts Dr. Haryanto R. Putro and Dr. M. Buce Saleh, Faculty of Forestry at Bogor Agricultural University (IPB), Indonesia, for their very encouraging and fruitful dis-cussions. Without their valuable time the core part of this research would have lacked real essence. I am also thankful to Centre for International Forestry Research (CIFOR), Bogor, Indonesia and its staffs for providing me necessary research materials and CDs. I am also thankful Dr. Alan Brown, who was our programme director, but left us in between to stay with God. He was very kind and having keen interest in his subject. I will be taking back his vision, on bringing novelty & interesting things to student (like creativity test), to IIRS students in India. My sincere thanks and gratitude to our initial student adviser, who later became our Programme director, Mr. Gerrit Huurneman. He is always a cheerful man and always having wonderful sense of humour to make any discussion a laughable. My sincere thanks to Dr. Yola Georgiadu, for her continuous effort in making our presence here very fruitful and making us always remember our institute’s future in bringing back a wealth of knowledge to coordinate our module. I am also greatful to all the staffs of ITC, from whom I gained wealth of understanding in many fields. Thanks to Mr. Mark Noort, for his support and help in making me comfort during the prob-lems faced in bringing my wife here. Thanks also to Ms. Sabine Maresch, who joined the Project team in 2002, for her immediate action/help whenever I end up with little administra-tive hurdles. Also I am thankful to Mr. Erd Blenke, our Cluster Manager, for his timely sup-port and help all the time. It is a mistake, if I not mention the kind, warm and efficient help


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provided by all secretaries, Educational Affairs staffs, help desk, hotel and facility manage-ment, especially Bettine Geerdink who still radiates energy at this age, hats off to her. Thanks to all my Indian colleagues/friends who played a major role in keeping us culturally warm. It is Ms. Vidya Natarajan, wife of former rector Dr. Karl Harmsen, who has been the eye of the storm in keeping us united at every possible occasion. Her two sweet kids get much credit in accommodating outsiders without a second thought. Her tireless effort with kindness and affection in making parties for 20 people at her house is an un-imaginable courtesy out-side India. Her presence cannot be forgotten easily and my wife joins me in saying our heart-felt thanks and wishing her a wonderful happy days. I am also greatful to my wife; her presence made my days a pleasant and wonderful one. Her tireless, consoling support during my late night studies, programming and in making my points clear for presentations, are unforgettable. Also my heartfelt thanks to her parents and her family members for their encouraging words always. Also the prayers from my parents and family members are appreciated with sincere heart. Last but not the least, thanks to all my GFM.2-2001 friends whose company was enjoyable and memorable. Also thanks to many of our old-Indian friends & new ITC friends who have kept us in touch through e-mails and discussions here and there, inside and outside of ITC. Finally my heart’s deep submission to Almighty and My Masters, whose teaching and bless-ings gave courage always and in making my every atoms move in the right path.


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ABSTRACT “Forest” plays a multi-dimensional role in maintaining many global processes, therefore, at-taining Sustainability in Forest Management is considered as a crucial and foremost problem in hand for many national and international institutions. The Measurement of Sustainability will benefit the Forest Management Units to attain a Certification Label, which will authenti-cate the products coming from such units to the global market. This certification procedure involves hierarchical evaluation of many parameters, which are defined in a vague manner using crisp verbal conditions. Currently Multi-Criteria Decision Making approaches like Ranking, Rating and Analytical Hierarchical Process (AHP), are generally used for evalua-tion. However, these approaches and most of the spatial models deal everything numerically and hence while integrating numerical compensation occurs, which is not representing true environmental interactions. Also they do not allow considering Expert’s Confidence, Attitude and Knowledge. In this research 4 different approaches: 2-tuple fuzzy linguistic approach, Fuzzy-AHP, Fuzzy Reasoning approach and Type-2 Fuzzy Reasoning approach, are modelled to suit the present system. They are also analysed for the possibility of removing existing hurdles and to check the credibility of each of them in certification process. It is found that Fuzzy Reasoning based approaches gives much more flexibility, transparency and full control on the processes in-volved in achieving the rational sustainability assessment. In overall, this research shall pro-vide a major direction for the potential utilization of fuzzy based approaches in assessing sus-tainability of forest management. KEY WORDS: Fuzzy, Sustainability, Forest Management, Uncertainty, Expert Knowledge


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TABLE OF CONTENTS

Acknowledgement………………………………………………………………………..I Abstract………………………………………...……………………………………….III Table of contents……..………………………………………………………………....IV List of Tables…………………………………………………………………….………V List of Figures……………...…………………………………………………………..VII List of Appendices…...………………………………………………………………..VIII Abbreviation……………….……………………………………………………….…VIII

1. Chapter I: Introduction .......................................................................................................1 1.1. Global Concern on Sustainability.............................................................................. 1 1.2. Problem Statement..................................................................................................... 1

1.2.1. Measuring Sustainability ................................................................................... 1 1.2.2. Need for Sustainable Forest Management......................................................... 2 1.2.3. Need for Fuzzy Logic........................................................................................ 2

1.3. Role of Remote Sensing and GIS .............................................................................. 3 1.4. Research Objective.................................................................................................... 4 1.5. Research Questions ................................................................................................... 4 1.6. Structure of the Thesis............................................................................................... 4 1.7. Assumptions and Scope of the research .................................................................... 4

2. Chapter II: SFM System Survey.........................................................................................6 2.1. Survey on Sustainability, Certification, Criteria & Indicators .................................. 6 2.2. Survey on MCDM methods in Sustainable Forest Management .............................. 7 2.3. Survey on Fuzzy Decision Making ........................................................................... 9

3. Chapter III: StudyArea & Certification Scheme ............................................................11 3.1. Study Area............................................................................................................... 11

3.1.1. Global importance ........................................................................................... 12 3.2. Reasons for choosing the study area and System of C&I........................................ 12 3.3. Framework of Forest Certification .......................................................................... 13

3.3.1. Certification Procedure.................................................................................... 13 3.3.2. SFM Assessment Processes............................................................................. 14

3.4. Technique for Assessment: Analytical Hierarchical Process (AHP) ..................... 15 4. Chapter IV: Methodology..................................................................................................21

4.1. Framework of decision processes............................................................................ 21 4.1.1. Non-spatial decision path ................................................................................ 21 4.1.2. Spatial decision path........................................................................................ 22

4.2. 2-Tuple Fuzzy Linguistic Approach........................................................................ 26 4.2.1. Methodology.................................................................................................... 26

4.3. Fuzzy AHP .............................................................................................................. 28 4.3.1. Methodology.................................................................................................... 28 4.3.2. Extension to suit LEI System .......................................................................... 29 4.3.3. Advantage of this Process ............................................................................... 29

4.4. Fuzzy Reasoning Approach..................................................................................... 30 4.4.1. Linguistic Variable, Linguistic Classes and Fuzzy set .................................... 30 4.4.2. Measurement & Standardisation Process ........................................................ 30


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4.4.3. Fuzzy Membership function and its interpretation.......................................... 33 4.4.4. Knowledge Building........................................................................................ 34 4.4.5. Expert Rule Acquisition .................................................................................. 34

4.4.6. Role of AHP in Fuzzy Reasoning Model........................................................ 39 4.5. Cognitive Mapping Process..................................................................................... 39

4.5.1. Methodology.................................................................................................... 40 4.5.2. Advantages of this Process .............................................................................. 40 4.5.3. Future Extensions ............................................................................................ 41

4.6. Type-2 Fuzzy Logic Approach................................................................................ 41 5. Chapter V: Analysis, Results & Discussion ....................................................................43

5.1. Analytical Hierarchical Process (AHP) Evaluation................................................ 43 5.2. 2-Tuple Fuzzy Linguistic Approach........................................................................ 44 5.3. Fuzzy Analytical Hierarchical Processing (Fuzzy-AHP) ........................................ 47 5.4. Evaluation in Fuzzy Reasoning Approach .............................................................. 50

5.4.1. Cognitive Mapping Process............................................................................. 52 5.4.2. Sensitivity Analysis ......................................................................................... 60

5.5. Type-2 Fuzzy Logic Approach................................................................................ 65 5.6. Overall Comparision ............................................................................................... 76

6. Conclusions & Recommendation ......................................................................................78 7. References ...........................................................................................................................81

LIST OF TABLES:

Table 3.1 Final SFM Grade Making Process 15 Table 3.2 AHP Comparison Scale 16 Table 5.1 Actual & Passing Performance of Test Data 43 Table 5.2 AHP integration results of Actual & Passing Performance 44 Table 5.3 Performances & Grades of All sites 44 Table 5.4a 2-Tuple Fuzzy Linguistic Approach Input Preparation (Fuzzification & chi

function) 45

Table 5.4b 2-Tuple Fuzzy Linguistic Approach Input Preparation (Delta function) 45 Table 5.5 2-Tuple fuzzy Linguistic Approach Final Performance Evaluation Steps

(Site-1) 46

Table 5.6a Results of FUZZY-AHP using Vector Matching Function 48 Table 5.6b Results of Modified-FUZZY-AHP using Vector Matching Function 48 Table 5.7 Results of FUZZY-AHP using Ideal Position Approach 49 Table 5.8 Steps involved in “Area_Management” Fuzzy Reasoning Model (Site-1 Ac-

tual Data) 50

Table 5.9 Steps involved in “Forest_Management” Fuzzy Reasoning Model (Site-1 Actual Data)

51

Table 5.10 Integration of AM & FM outputs in “Forest Resources Sustainability” Fuzzy Reasoning Model (Site-1 Actual Data)

51


VI

Table 5.11 Output From the Fuzzy Reasoning Model 52 Table 5.12 Role of Verifiers in the Forward & Backward Routes 58 Table 5.13 Consistency Check between Experts Rules and His Views on Ground Inter-

action 59

Table 5.14 Fuzzy Model output from membership curve with different attitudes 63 Table 5.15a Sensitivity of the Model with respect to input variations in Indicator P1.3 64 Table 5.15b Sensitivity of the Model with respect to input variations in Indicator P1.1 65 Table 5.16 Type-2 Fuzzified values of Inputs from Site-1 69 Table 5.17a Possible Rules applied to Site-1 data over AM 69 Table 5.17b Fuzzy Inferencing applied to Site-1 data over AM 70 Table 5.18 Possible Rule combination at FRS level (Site-1) 70 Table 5.19 Type-2 Rule Strength Evaluation for Rule-1 in Area Management Part of

Site-1 71

Table 5.20 FRS evaluation & Centroid Statistics obtained from Type-2 Fuzzy Approach (Site-1)

72

Table 5.21 Outputs from Type-2 Fuzzy Logic using Membership curves having Uncer-tainty in the Base (X-Range) Only

73

Table 5.22 Outputs from Type-2 Fuzzy Logic using Membership curves having Uncer-tainty in the Base (X-Range) & Uncertainty in Highest Membership value

74

Table 5.23 Input data arranged in importance order* 75 Table 5.24 Results from different approach 75 Table B.1a The Original Verbal Pairwise Comparison Expected from Experts 91 Table B.1b Numerically converted Pairwise Comparison Matrix 91 Table B.2 The Pairwise Comparison Matrix for Each Indicator for Site 1 92 Table B.3a Performance Calculation (for Indicator P1.1 of Site-1) 93 Table B.3 Relative Performance of Each Norm under Each Indicator for Site-1 94 Table B.4 Pairwise Comparison Matrices, Relative Performance & Weights for Site-2 95 Table B.5 Pairwise Comparison Matrices, Relative Performance & Weights for Site-3 96 Table B.6 Pairwise Comparison Matrices, Relative Performance & Weights for Site-4 97 Table C.1 Fuzzy Pairwise Conversion 98 Table C.2 Reciprocal Fuzzy Pairwise Conversion 99 Table C.3 Fuzzy Arithmetic 99 Table C.4 Fuzzified Pairwise Comparison Matrix of Indicator P1.1 (Site-1 Data) 104 Table C.5 Fuzzy Performance values & (Modified) Fuzzy-AHP Hierarchical weights

(Site-1 Data) 105

Table C.6 (Modified) Fuzzy AHP Performance Calculation (Site-1 Data) 106 * �� Represents the Tables printed in Colour


VII

LIST OF FIGURES:

Figure 3.1 Study Area Locational Information * 11 Figure 3.2 Hierarchical Framework of SNPFM 18 Figure 3.3 Certification Process in Indonesian Scheme 19 Figure 3.4 The portion of SFM hierarchy chosen for the present study 20 Figure 4.1 Non-Spatial Effect Table 22 Figure 4.2 Spatial Effect Table 23 Figure 4.3 Integrating Paths for Heterogeneous data* 23 Figure 4.4 Possible Improvements to the current certification system* 25 Figure 4.5 Standardisation possibility for verifiers 31 Figure 4.6 Spatial Aggregation Procedure for the Verifiers in Indicator P1.1 32 Figure 4.7 Fuzzy Linguistic Classes & Membership curves 33 Figure 4.8 Conceptual Skeleton of the research approach* 37 Figure 4.9 Architecture of Fuzzy Reasoning Model 37 Figure 4.10 Implemented Fuzzy Reasoning Model* 38 Figure 5.1 Relative Percentage of Contribution from Different Parameters at different

levels (Using Different Membership functions) 55

Figure 5.2 Causal Relationship Diagram of Different Verifiers* 56 Figure 5.3 Direct & Central Forces Exerted By ‘Stake Holders Agreement’ Verifier* 57 Figure 5.4 Membership Curves with Different Confidence Levels 61 Figure 5.5 Membership Curves with Different Attitudes 62 Figure 5.6 Type-2 Fuzzy Membership Functions & its ranges (Uncertainty in the Base

x-range Values) 67

Figure 5.7 Type-2 Fuzzy Membership Functions & its ranges (Uncertainty in the Base x-range Values & Uncertainty in Highest Membership Value range)

68

Figure C.1 Alpha-Cut Example 100 Figure D.1 Fuzzy Mamdani Inference over Indicator P1.6* 109 Figure D.2 Defuzzification Process 110 Figure E.1 Number of Rules required at Different Levels of LEI system 112 Figure E.2 Decision Tree used for Indicator P1.1 113 Figure E.3 Decision Tree used for Indicator P1.2 113 Figure E.4 Decision Tree used for Indicator P1.3 114 Figure E.5 Decision Tree used for Indicator P1.4 115 Figure E.6 Decision Tree used for Indicator P1.5 115 Figure E.7 Decision Tree used for Indicator P1.6 115 Figure E.8 Decision Tree used for the criteria Area Management (AM) 116 Figure E.9 Decision Tree used for the criteria Forest Management (FM) 117 Figure E.10 Decision Tree used for the criteria Forest Resources Sustainability (FRS) 117 Figure F.1 Gaussian Interval Type-2 Fuzzy Membership Function with Upper and

Lower FOU* 119

Figure F.2 Gaussian Membership function - Uncertainty in Mean 123 Figure F.3 Gaussian Membership Function - Uncertainty in Standard Deviation 123

* �� Represents the Figures printed in Colour


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LIST OF APPENDICES:

Appendix A-I Description of LEI Indicators, Verifiers and its Intensity Scale 86 Appendix A-II Verifiers Preferred by Experts & their possible Standardization Procedure 88 Appendix B Input data sets for AHP approach used in current LEI system 91 Appendix C-I Detailed Modified Methodology of FUZZY-AHP 98 Appendix C-II Step By Step Execution Of Fuzzy AHP 103 Appendix D Fuzzy Set Theory & Fuzzy Logic Concepts 107 Appendix E Expert Rules used at different levels

(Verifiers, Indicators, Criteria & Principle level) 111

Appendix F Basic Terminologies and concepts of Type-2 Fuzzy Set 118 Appendix G Software Used & Future Continuation 126

ABBREVIATION:

TERM EXPLANATION ACTUAL The Current Ground Performance of the FMU AHP Analytical Hierarchical Process AM Area Management C & I Criteria and Indicators CRD Causal Relationship Diagram CIFOR Centre for International Forestry Research FM Forest Management FMU Forest Management Unit FOU Foot print of Uncertainty FRS Forest Resources Sustainability FRM Fuzzy Reasoning Model FSC Forest Stewardship Council GIS Geographical Information System/Sciences ISO International Standards Organisation ITTO International Tropical Timber Organisation LEI Ecolabel Institute of Indonesia MCDA Multi-Criteria Decision Analysis MCDM Multi-Criteria Decision Methods PASSING The minimum Performance required by the FMU to get passing grade PCM Pairwise Comparision Matrix RS Remote Sensing SFM Sustainable Forest Management


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1. Chapter I: Introduction

1.1. Global Concern on Sustainability

The earth is at its worst state of flux - having increased number of natural disasters through floods, forest fires, Elninos, ozone depletion, land degradation and desertification -challenging the human existence. The human intelligence, which is at its elegance than ever before in the history of humanity, has provided numerous advanced ways to monitor such complex behavior of the earth at any place. But in vain the hidden imbalanced developments have been causing serious impact on the environment at the back door. These global changes and need for healthy, productive life of present generation and sustain-ing their environment for future generations was echoed globally through Brundland report in 1987 (WCED, 1987) and Rio Declaration in 1992 (UNCED, 1992). These declarations have given open invitation to every nation to come out with their own poli-cies/standards/legislations in accordance with their own environment and cooperate in close hand with international laws in providing equal share on standard of living without disparity, without damaging ecosystem of theirs and neighbors. From then the concept of sustainability has been taken seriously in all the developmental activities over the globe. Though more than 200 international/multilateral environmental agreements are in force, sys-tematic implementations at various domains – scientific, technical, institutional and political, are not yet fully achieved (Changchui, 1999). Recently it was observed that the carry forward efforts to inflame sustainable development resolutions taken at the historical UNCED Summit 1992 has been extremely unsatisfactory (UN-WSSD, 2002) and Johannesburg summit 2002 was stressing more of actions and results. In this regard the measurement of sustainability in Forest Management is one of the field in realizing the vision of WSSD 2002.

1.2. Problem Statement

1.2.1. Measuring Sustainability

Sustainability is the conceptual aspect of set of processes aimed to deliver desired services over long period of time. Study on sustainability requires an interdisciplinary approach over social, ecological and economic sciences. Measurement of such diverse states of systems is a difficult and complex process that requires dedicated researchers and creative research across many fields. Understanding, designing and managing these systems on a sustainable basis over an entire life cycle is a major challenge facing this generation. Though there is no meas-uring yardstick by which we can assess sustainability, but by emulating human expertise and systematic approach we can handle imprecise situations through fuzzy logic to give clear pic-ture of reality.


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1.2.2. Need for Sustainable Forest Management

“Forest” has been the key element in maintaining sustainability of many of the global phe-nomena. Since the human dependence on forest is inevitable in many aspects, the chances of getting it degraded are many folds and at the same time we cannot completely stop using for-est products. In realizing this international organizations/summits have made “Environmental friendly products” and “sustainable use of forest” a global issue. Forest management is re-sponsible for guaranteeing sustainable use of forest in terms of Economical, Environmental and Social welfare. To know whether the forest is sustainably managed or not, it has to be certified. The “Ecolabel” certification is one of the instruments, which authenticates that the forest product is coming from sustainably managed forest. In the sustainable forest manage-ment (SFM) evaluation, set of principles (fundamental reason as a basis of action), criteria (which adds meaning to principle without itself being a direct measure) and indicators (any variable to infer the status of criterion) are designed in a hierarchical levels in such a way that they serve as a tool to promote SFM as a basis for monitoring and reporting or as a reference for evaluating sustainability of actual forest management (Bueren and Blom, 1997). All the earlier studies related to sustainability assessment in SFM (Prabhu et al. 1999, Men-doza & Prabhu 2000, Alan 2002) have used different multi-criteria decision making ap-proaches like ranking method, rating method and Analytical Hierarchical Process (AHP). Ranking helps to arrange criteria in the order of their importance. In practice if more than 9 parameters exists, discriminating conceptual importance becomes difficult. In rating method, the decision maker distributes 0 to 100 points across the evaluation criteria. More the points a criterion gets, more relative importance it possesses. Advantage of using ranking or rating is their simplicity but both lack theoretical foundation (Malczewski J, 1999). Though AHP gives more insight in terms of assessing consistency of the expert judgment (Mendoza G.A & Prabhu R., 2000), it involves complexity and intense comparison of every pair of parameters in each hierarchical level. Also in AHP numerical compensation occurs in the final result, which means that the bad performance of one parameter can be compensated by good per-formance of another parameter, but in reality the area affected by forest fire cannot be com-pensated by having good Early Warning system. Also there is no explicit way by which we can include confidence and attitude of the decision maker in AHP.

1.2.3. Need for Fuzzy Logic

It is a well-known fact that decision-making in forest management involves different envi-ronmental aspects, which are in reality fuzzy. In such applications main concerns lies with the meaning and relation of information rather than with its measure. In such cases the proper framework for information analysis is possiblistic rather than probabilistic in nature (Zadeh, L.A 1978) and hence theory of fuzzy sets provides a natural basis for this research. In SFM, fuzziness comes into picture in all level, starting from input, in constraints, in goal to finally in decision. Since sustainability is not quantitatively measurable by nature and also it


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involves uncertainty and vagueness, fuzzy logic would provide a way to systematically for-mulate a base for quantifying such information. The indicators and verifiers used on the ground are of unsharp nature. The rules used currently for checking different verifiers are crisp (Appendix A-I), but in reality their boundary is unsharp (imprecision in description), so fuzzy sets will help to model such classes. The evaluation process involves Expert Knowl-edge; so fuzzy reasoning provides a structured and consistent way to frame inference rules. Many researchers have investigated applicability of fuzzy logic in spatial processes (Burrough, 1989, McBratney and De Gruijter 1992, A-Xing Zhu, 1999, Luc A. Andriantiat-saholiniaina, 2000). But these researches have taken the expert rule as a thumb rule and they have neither checked the consistency of the expert knowledge nor provided a way to analyse them. Also they have not addressed uncertainties associated with the membership function (as variation of membership curve) in terms of shape, size and dimension. Also the previous re-searches in SFM have not attempted to include Decision Makers confidence and attitude in the decision process. Since the parameters, their meaning, relation with other parameters and decision making hierarchies varies with place to place and application to application, the same rules and functions cannot be applicable universally, but methodology can be universal and in this sense the present research would attempt to deal in great amount on intricacies of fuzzy methodology in order to make the decision process transparent, consistent and applicable anywhere.

1.3. Role of Remote Sensing and GIS

In modern resource management, remote sensing (RS) and geographic information system (GIS) can play a major role in the compilation, manipulation, presentation and monitoring of spatial data. Vast literature is available in this regard, listing them here is out of focus. In our study RS & GIS can be used to quantify the verifiers like identification of proper allocation of any area of land to a forest zone can be analysed by overlaying interacting biophysical (e.g. vegetation, slope, elevation) and socio-economic (e.g. land ownership, intended land use) fac-tors. Remote Sensing and GIS in combination will be an inevitable part of input preparation and standardization process of this study. It has been observed that limited spatial data layers are used in most of the researches in natu-ral resources management related studies to explore a methodology/models and this may be due to the vastness of spatial data storage and intensive analysis time. But in Sustainability related work we have huge amount of indicators & verifiers and if we deal everything in spa-tial domain then we would not be able to dynamically simulate the process & test the meth-odology efficiently and hence in this research we have considered all possible values & com-bination of different spatial layers rather than their location so that we will be able to investi-gate the role of fuzzy methodology in a better manner.


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1.4. Research Objective

The overall objective of this study is to explore the role that fuzzy logic can play in improving the decision making process in assessing sustainability of forest management for the purpose of forest certification. In this process the study sets the following objective

��Develop a methodology to integrate heterogeneous spatial, non-spatial data and expert knowledge to assess sustainability of forest management using fuzzy logic

1.5. Research Questions

In meeting the objective of this study, following questions shall be asked

��What sort of approach shall be used to transform spatial and non-spatial data into value judgements?

��How shall integration/process be done over value judgements? ��How shall we use expert’s knowledge in the process? ��To what extent fuzzy approach can improve the process with reference to old

existing systems? ��How shall sensitivity of the approach be measured?

1.6. Structure of the Thesis

The present research is elaborated in six chapters. Chapter 1 deals with the basic reasons be-hind this research, its objective and research questions. Chapter 2 explores existing literatures related to the various components associated with the research. Chapter 3 clarifies the study area chosen and reason for that. Also it gives the complete narration of present Sustainable Forest Management Certification system used in Indonesia. Chapter 4 depicts the methodolo-gies considered for this research, advantages of each of them and the expected results from each approach. Chapter 4 gives theoretical solutions to first three research questions. Chapter 5 illustrates the analysis done over different methods, results and discussion. Chapter 4 & 5 in combination can provide tested, practical answers to all research questions. Finally Chapter 6 describes the conclusions & recommendation by furnishing focused answers to the research questions.

1.7. Assumptions and Scope of the research

��In order to develop & test the methodology, study area has been chosen in Indo-

nesia where the SFM process is in practice and hence we would be able to get sufficient knowledge from the experts involved and also there is a need for im-proved efficient alternative to the current decision process.

��The present study assumes that the existing principles, criteria and indicator are

good enough and valid for the study area.


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��Though remote sensing and GIS is an inevitable part of input preparation and standardization process, the focus is made to fuzzy methodology development & testing in this research.

��Since the SFM decision process involves large amount of parameters, develop-

ment of fuzzy methodology will be done only on part of the decision making hi-erarchy to put more focus on integration rather than organizing information.

��This study can be extended to compile full certification system in future and shall

provide major direction for the development decision support system in this line.

��This study methodology can be applied to any spatial and non-spatial decision making processes and sustainability assessment apart from forestry applications.


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2. Chapter II: SFM System Survey

2.1. Survey on Sustainability, Certification, Criteria & Indicators

Since it has been believed that gain in Economic Development means loss in Environment ( Daly, 1987), the issues of Economic Development and Environmental Protection have be-come two major parameters of all the global, regional and national policies throughout the world. This idea of opposite poles will not lead the humanity for long term survival and in an indirect way of making this believe false, the concept of sustainability was first used in the international forum by Brundland report (WCED,1987) which is basically because of rapid degradation of environment. As per its definition, ‘the sustainability is meeting the require-ments of present generation without compromising the ability of future generations to meet their own needs’. In short “the whole idea of sustainability is to balance the two forces (economy and environment) in such a way that it leads a third force i.e., social well being, to a better condition for longer duration”. Overall sustainability is the derivative of amalgamation of economical, environmental and social processes. The sustainability in forest management is one of the active domains due to its associated profound economic linkage. The concept of sustainable forest management (SFM) was first stated in the Chapter 11 of Agenda 21 of UN conference on Environment and Development (UNCED,1992, Adrian Newton 1995, Mendoza and Prabhu 2000a, 2000b). Also Dr. Adrian Newton refers to Schmutzenhofer, 1992 for the fact that concept of sustain-able forest has been used as early as 1804 in Germany. International Tropical Timber Or-ganization (ITTO, 1992) has been considered as first to recognize standards explicitly related to sustainable forest management during 1990 (Agung,2000), which was later referred as ba-sis for many other later initiatives. In order to deal with Sustainability in Forest management the concept of Forest Certification is considered as an agreed upon process by many global initiatives. Forest Certification deals with the measurement of Economical, Environmental and Social sustainability of a forest management unit under consideration by authenticated third party evaluators, who are experts in the respective domains. According to Upton and Bass (1995), Environmental sustainability leads ‘the ecosystem able to support healthy organisms, whilst maintaining its productivity, adaptability and capability to renewal’ and this makes the forest management to respect and develop along with natural processes; Social sustainability is keeping the relationship between development and social norm at a balanced state without breaking the community’s tolerance limit; Economic sustainability says that the group(s) in question gets their share of benefit and also keep some share of capital for generations to come. Forest Certification process is comparable to “auditing” process in normal life. Forest Certifi-ers follows pre-defined set of guidelines, which uses Principles, Criteria and Indicators while making assessment. Development of Criteria and Indicators (C&I) has been considered as


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significant step for the measurement sustainable forest management (Mendoza and Prabhu, 2000b), because it helps in providing timely vital information about the Forest Management Unit involving many stakeholders and government policies (Prabhu, 1999). Different interna-tional organizations and initiatives have developed their own Criteria and Indicators for the Evaluation of SFM in forest certification as per their domain of interest and policies of local influence, but in an un-coordinated way during 1990-1994 (Prabhu, 1999). Forest Steward-ship Council (FSC) and International Tropical Timber Organization (ITTO) have been con-sidered as the guiding sources for many of the C&I sets developed by other initiatives though which were not similar (Prabhu, 1999, Mendoza and Prabhu, 2000b, LEI, 1998,2000). C&I developed by Lembaga Ecolabel Indonesia (LEI) follows exemplified inspiration of FSC and ITTO. As per International Institute for Sustainable Development (IISD, 1996), a survey con-ducted in mid-96 has revealed that more than 30 countries had already implemented initia-tives for eco-labeling or certification of one or other, without considering ISO 14000, since it is only recent development in late 2000s. All the initiatives and its developed C&I set have the common framework revolving around the concepts of Principle, Criteria and Indicator (Mendoza and Prabhu, 2000b). International Institute for Sustainable Development (IISD, 1996) has divided the international initiatives for measuring SFM into two broad categories as C&I and Certification. Certification requires agreed C&I, while C&I do not imply any formal certification system. Certification is not wel-comed by some countries, but rather they energetically pursuing agreement on C&I. IISD (1996) and Adrian Newton (1995) have given detailed list of major Certification systems and C&I. Availability of different C&I for assessing sustainability have to be tested for effective-ness and efficiency. Center for International Forestry Research (CIFOR) have been actively involved in this interest group to produce a regionally acceptable set of C&I and develop a mechanism for objective evaluation. It is found that relatively little work has been done to implement C&I to achieve Sustainability and the reason may be huge amount of verifiers in-volved, which are having poor, vague definition and imprecise, verbal measurement possibili-ties and finally sensitive evaluation process.

2.2. Survey on MCDM methods in Sustainable Forest Management

Multi-Criteria Decision Making (MCDM) methods have given leeway to practically imple-ment SFM evaluation process. MCD problems generally engross set of alternatives which are evaluated on the basis of conflicting and incommensurate criteria, which are qualitative, quan-titative or both (Malczewski, 1999). In the domain for SFM, the MCDM approach is consid-ered potential because of its demonstrated ability to integrate multiple criteria, different groups, experts, with-standing spatial, non-spatial & inexplicit data and most importantly transparent to the participants (Marjan Van Herwijnen 1999, Mendoza and Prabhu 2000b, Sharifi 2002). Many overview articles are available related to MCDM, also about its merits and demerits ( Roy,1971; MacCrimmon,1973; Triantaphyllou,2000). Vast literatures are available in the spa-tial and non-spatial MCDM decision analysis (Keeney and Raiffa 1976, Saaty 1980, Malczewski 1999, Marjan 1999, Mendoza and Prabhu 2000a,b). The MCDM methods can be


8

categorized into two groups as MADM (Multi-Attribute Decision Making) and MODM (Multi-Objective Decision Making). Each of which is further divided into Single-Decision Making or Group Decision Making, which intern subdivided into Deterministic, Probabilistic and Fuzzy Decisions (Malczewski, 1999). In the domain of SFM, Group Decision Making takes place, by which all the elements are quantified in order to fit into a deterministic ap-proach but in reality the SMF involves vague and imprecise inputs and need fuzzy based deci-sions. In SFM, most frequently used methods are Analytical Hierarchical Process (AHP), Ranking and Rating methods, which all makes use of Weighted Sum or Weight Product as their final aggregation model. The Analytical Hierarchical Process (AHP) was first introduced by Saaty (Saaty 1977,1980), to eliminate the problems associated like non-availability or mixed data while making decision. His approach takes the user through a simple process of comparing only two elements at a time, in terms of achieving the required criteria, called Pairwise-Comparison. He has taken the scale range of 1/9, 1/7, 1/5,1/3,1/1 to 1,3, 5, 7, 9 meaning abso-lutely non-importance (1/9) to absolute importance (9). This approach have invoked many applications due to its easiness in obtaining input data and in 1994 more than 1000 references were cited (Triantaphyllou,1990; Saaty,1994). But this is also not void of loopholes. Belton & Gear (1983) and Triantaphyllou (2001) have shown that even AHP has the possibility of rank reversal when there is a change in number of alternatives and they also proposed im-provements in AHP. Freerk A. Lootsma (1997, 2002a, 2002b) has done elaborative work in producing enhanced methods like additive & multiplicative AHP, which have taken rational human inducted scales for the judgement. Also AHP has a drawback of having increased number of comparisons when number of entities increases. For example if there are ‘n’ alter-natives is to be examined in terms of 1 criteria then number of pairwise comparison needed are [n (n-1)/2] and if ‘n’ alternatives are to be compared in terms of ‘m’ criteria in a same sin-gle level then number of pairwise comparisons required are [m(m-1)/2 + m (n (n-1)/2] (Trian-taphyllou, 1999). If we have 3 alternatives say a1, a2 and a3 and it is to be compared for 1 criteria then out of possible 9 comparisons the combinations which are really needed are only 3 comparisons a1a2, a1a3 and a2a3 (because a1a1, a2a2, a3a3 will be always 1 and a21, a31, a32 can be de-rived as a reciprocal of a12, a13, a23 respectively). If we have 10 alternatives and 10 criteria, then we need to do 550 comparisons. Triantaphyllou (1999) has introduced Dual Comparison approach which uses a pairwise-comparison matrix for every alternative rather than for each criteria and this method need less number of pairwise comparison if number of alternatives is greater than number of criteria plus one. Ranking and Rating methods are very simple and straightforward, but do not have any mathematical base. Another major pitfall in ranking and rating is when the user gives a quantitative value to a qualitative variable, the interpretation by the process is treated in ‘ratio scale’, which is considered as multiplicative rather than addi-tive. The conventional approach in economics using Cost-Benefit analysis cannot be used in environmental process because we cannot equate/compensate the environmental loss monetarily. The major hindrance associated with MCDM approaches are that they depend largely upon the input data and standardization methods. All the Environmental related decision involves


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multi-dimensional criteria, which are mixed (qualitative and quantitative), which do not have universal inter and intra boundary definitions. Also there are several standardization methods, which affect the final decision invariably, and there is no obvious benefit of any single method over other (Hwang and Yoon, 1981, Howard, 1991). Also the selection of standardi-zation methods plays a key role in explaining the behavioural variation of the criteria under scrutiny, which means better understanding of each criterion on ground is needed, which is mainly lacking in environment related criteria. Sensitivity analysis is another very important part of any decision making process, which explains the validity of the chosen approach. But most of the available MCDM methods do not say by itself, which is the most critical criterion or critical performance value, means how small variation (absolute or relative) in weights or input data will affect the best ranking alter-native or may completely change the overall or any ranking orders. The work by Masuda (1990) about sensitivity analysis of multi-level hierarchy and procedure by Armacost and Hosseini (1994) to identify most critical criterion in a single level hierarchy are referred as the important step in sensitivity analysis in AHP. But the improvement and innovative work by Triantaphyllou (1997) have given efficient sensitivity analysis procedures, for knowing the most critical criterion as well as the amount of change needed in weight and performance value to alter the final ranking, in a decision making process under Weighted Sum Model (WSM), Weighted Product Model (WPM) and AHP approaches. But AHP is criticized due to its inability to adequately deal with inherent uncertainty, ambiguity of the pairwise compari-son process, because it uses crisp numbers (Hepu Deng, 1999)

2.3. Survey on Fuzzy Decision Making

At this juncture of understanding-combat between human and environment, fuzzy based deci-sion process comes handy to contribute making efficient decision. Triantaphyllou et al (1990) have encountered more than 1800 references dealing with fuzzy set theory in scientific prob-lems. Much of the fuzzy focus is paid on Artificial Intelligence researches. Recent studies have shown the applicability of fuzzy logic and its efficiencies in spatial, non-spatial proc-esses (Burrough, 1989, McBratney and De Gruijter 1992, Triantaphyllou & Chi-Tun Lin 1995, A-Xing Zhu 1999, Luc A. Andriantiatsaholiniaina 2000). Buckley (1985) and Laarho-ven & Pedrycz (1983) have extended the AHP to include imprecision and uncertainty using fuzzy approaches. Limitations of this approach lead to a new fuzzy-AHP approach by Hepu Deng (1999). Hepu Deng (1999) has proposed an elegant synthesized fuzzy pairwise comparison approach, which is the amalgamation of fuzzy set theory, AHP, fuzzy extent analysis, alpha-cut concept, ideal solution and vector matching function. This approach provides a user-friendly way of incorporating DM subjectivity and imprecision of evaluation process. In Fuzzy approach, vagueness and imprecision associated with qualitative data can be repre-sented more logically, using linguistic variables and overlapping membership functions in the uncertain range, than using conventional MCDM path. Also the data, which are measured in different units, can be used directly without any additional need for standardization. The ma-


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jor advantage of fuzzy logic is that it can be used both as compensatory and non-compensatory in a single model at different context, by using inferences through rules ex-tracted from the experts. In this view Luc A.2000 studied the usage of fuzzy logic in sustain-ability assessment. Interestingly though all his inputs were easily quantifiable in nature, he has chosen fuzzy approach to include assumed vagueness and impreciseness in the interpreta-tional measure while representing sustainability. Herrera F., and Martinez L., (1999) has ex-plained the use of elegant 2-Tuple fuzzy linguistic approach when input criteria are of mixed nature. Cornelissen et al (1999) have given the conceptual idea of how to include fuzzy set theory in assessing sustainable development and he has demonstrated a simple one level ex-ample of agricultural production sustainability. Though the fuzzy alpha-cut approach introduced by Zadeh in 1965 is mainly used in repre-senting uncertain knowledge under fuzzy based approaches, it mainly helps to incorporate only the uncertainty in the input data and hence output data, but it cannot handle the uncer-tainty in interpreting the meaning of input data. Membership function is used as a way to in-terpret the meaning of the input data and its strength. Hence the nucleus of fuzzy model is its membership functions and it is considered to be the strongest and weakest point of fuzzy set theory (Munda et al. 1992). Trial and Error approaches, neural back-propagation approaches are used to tune the membership function in control system applications, but in the sustain-ability assessment it would not be possible because we do not know the real outcome. In such case identification of sensitivity of the variation in membership function is important in order to have clear understanding about the uncertainties associated. Freerk A. Lootsma (1997), Klir and Folger (1988), Klir and Wierman (1998) and Jerry M.Mendel (2001) have de-scribed/discussed elaborately about the nature, causes and occurrence of uncertainty in fuzzy logic system. Since the normal fuzzy memberships does not include the embedded uncertainty associated with the defined range of input and degree of belonging, it shall not be considered as a com-plete uncertainty representation. In this regard Jerry M. Mendel (2001) and his PhD students have given a detailed in-depth study and explanation on type-2 fuzzy logic system, which in-cludes uncertainty within the usual fuzzy logic (which he calls as type-1 fuzzy logic). Type-2 fuzzy logic is a 3-D system of membership functions where usual primary memberships are given secondary grades of uncertainty weights as a 3rd axis, also having the polygonal base of primary memberships rather than single shape function. Type-2 fuzzy logic approach is com-plex and huge number of operations is required. Not a single study has been done in using this approach in forest management. Still not much work is done and much scope is left in Sustainable Forest Management in terms of effect of varying membership function, role of inference rules and how shall we in-clude Type-2 fuzzy set approach in representing uncertainty in the model. With these argu-ments the present study would aim to include total concept of fuzzy approaches from AHP to fuzzy AHP, type-1 fuzzy to type-2 fuzzy in order to identify the achievability and incorporat-ability of uncertainty in the domain of sustainable forest management.


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3. Chapter III:

StudyArea & Certification Scheme

3.1. Study Area

The area chosen for the current research is Labanan Forest Management Unit of Inhutani I located in Berau District Regency, North-western East Kalimantan province, Indonesia. The study province East Kalimantan is the least populated and one of the wealthiest and largest province of Indonesia. East Kalimantan has around 16.1 million ha of forest area, which is around 76% of its provincial area 21.1 million ha, and our test site manages around 15% of forest area (BFMP, 2000). The boundary of the study are P.T. Inhutani I concession unit lies between the latitude of 2o 10’ N and 1o 45’ N and longitude of 116o 55’ E and 117o 20’ E (Fig. 3.1). This management unit is owned by government as a part of its forestry business unit and the concession is done jointly with European Union under a project named “Berau forest Management Project” (BFMP).

Figure 3.1: Study Area Locational Information


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3.1.1. Global importance

Indonesia is a country with 17,000 islands spread near equator in Southeast Asia. Although it has only 1.3% (181 million ha) of world land surface, its tropical rich forest area (105 mil-lion ha in year 2000) is ranked 3rd in the world next to Brazil and Democratic Republic of Congo. Indonesia plays an important role for global biodiversity through contributing 11 per-cent of the world’s plant species, 10 percent of mammal species, and 16 percent of bird spe-cies. The majority of these species is spread over and depends on the country’s forests. Many millions of forest-dwelling or forest-dependent people also rely on Indonesia’s forests for their livelihoods (GFW, 2002). In the early 1970s, the development of the Indonesia’s wood-processing industries has detoriated its forest resources. Today, Indonesia is a significant producer of tropical hardwood logs, plywood and other boards, and pulp for papermaking. Indonesia produces around 120 million cubic meter of round wood and exports 1.5 million cubic meters every year (GFW, 2002). Over the past 50 years the deforestation has reduced 50% of the Indonesian forest badly. The rate of forest loss was 1million ha per year in 1980 and it rose to 1.7 million ha in 1990 and in 1996 it has reached 2 million ha per year (size of Belgium) (FWI/GFW, 2002). Serious threat is foreseen for the lowland tropical forests of Indonesia, which are richest in timber re-sources and biodiversity and if the current trend continues it will vanish Sumatra and Kali-mantan by 2010 (Holmes, 2000). Having such seriousness in hand, the government has to play a crucial role in avoiding environmental impacts and at the same time balancing coun-try’s economical sustenance through proper management and certifications. This can be only achieved with the proper forest management and in this regard the current research shall be used as a part of global programme.

3.2. Reasons for choosing the study area and System of C&I

First of all this research is mainly focusing on methodology development so it can be applica-ble to any study area. But for the initial development we have to have test site where sustain-ability assessment related with forest certification is being done. ITC students have been do-ing active research (Fauzi 2001, Wahyu 2001, Aguma 2002, Dahal 2002, Alan 2002) in this area and there is a project proposal in ITC over this area (Sharifi 2002) related to forest certi-fication process, for which this research will provide a major step. Spatial and non-spatial data for several themes are readily available. Importantly the study area is located in Indone-sia, which is having a major deforestation threat on tropical rain forests, which will have sig-nificant impact on global climate and biodiversity. Hence this study would be used for other sustainability purposes later to assess whole situation of the region. Also there is no single earlier work done using fuzzy logic in the study site. The main reason for choosing the Criteria & Indicators developed by LEI is that they follow the standards set by ITTO, FSC and also environmental management system set by ISO (Agung & Hinrichs, 2000). More over it is developed by considering existing national, local


13

situation and affairs of forest in Indonesia. Also local forest management team, LEI and gov-ernment are very much in need of improving the credibility of the certification system and in this aspect the present research would help in improving the decision making process. I come from India and in India there is no forest certification system currently. Also develop-ment of Criteria & Indicators for assessing the credibility of forest management unit is still in exploration stage. In this aspect the present research will also provide a major input and would help them in understanding and choosing the efficient methodology.

3.3. Framework of Forest Certification

The Ecolabel certification instrument in Indonesia is called Sustainable Natural Production Forest Management (SNPFM) Certification. The SNPFM certification aimed to assess the quality of forest management practice and provides recommendations for management im-provement if necessary. The SNPFM uses standard for Evaluation developed by Ecolabel Institute (LEI, 2000). In the sustainable forest management (SFM) evaluation, set of principles, criteria and indica-tors are designed in a hierarchical levels (Fig. 3.2) in such a way that they serve as a tool to promote SFM as a basis for monitoring and reporting or as a reference for evaluating actual forest management (Sharifi M.A., 2002). In SFM, three sustainability functions: Production, Ecology and Social, are considered at the top of the evaluation hierarchy as Primary princi-ples. Under this there are many Secondary Criteria and each of the criteria has number of ter-tiary indicators and these indicators are in turn assessed by verifiers on the ground. The veri-fier may be a map representing part of indicators requirement (like erosion or slope classes) or may be legal laws or some measurement.

3.3.1. Certification Procedure

The LEI certification process involves different teams co-ordinating with each other in high resonance, in order to fulfil the need of other, at different stages. The whole procedure, play-ers and stages are clearly depicted in the Figure 3.3 (Elim Salim et al. 1997). The key play-ers involved are Assessment Team, Expert Panel (I, II & III) including Indonesian Eco-labelling Institute (LEI). The major stages implicated in this scheme, as it occurs, are: Pre-field assessment, Field assessment & Certification Recommendation and Post field assess-ment. In the Pre-field assessment the Expert Panel I does the evaluation of documented materials, legal correctness, with respect to what is prescribed in Principles and Criteria of SFM and their decision will determine the undertaking of next stage. They also provide recommenda-tions to Assessment team for field verifications, if the pre-field assessment is cleared. In the next stage, field assessment is done by assessor team and they will submit the field evaluation report to Expert Panel II, who plays the major role in making the recommendation on ‘grade of Ecolabel’ based on overall performance of the management unit. Then the final stage is to communicate the recommendation given by experts to the public/stake holders through news-


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paper advertisement and other communication medium. This final stage will help to have transparency in the approach and to gain public/stakeholders validation/confidence and hence will avoid favours to private management units. In case of discrepancy at this stage Expert Panel III will be formed through multi-stakeholders involvement and discussions will be made accordingly.

3.3.2. SFM Assessment Processes

The total Sustainability assessment process consists of 3 major processes, each one of them are in itself a big task. First is determining relevant criteria and identifying proper indicators which can directly or indirectly reveal the associated hidden information related to sustain-ability principles. Second is attaching a value for each indicator; which is done through field assessment by experts from different discipline, by documental evidence and by discussion with stakeholders and community. Third and final step is processing the measured values, assessed FMU condition to determine the final ranking. In the view of MCDM approach, the SFM process in LEI system consists of only 2 alterna-tives. One alternative is the ‘passing alternative’, for which the experts will allocate some standard performance score for every indicator, from the knowledge of typology. This is the minimum requirement in order to qualify for certification. Another alternative is the ‘actual performance’, which gets the actual assessed performance value of the Forest Management Unit. Table 3.1 provides an easy overview of grades and its calculation ways. In the table the values P & Q are weighted sum of individual performances over different hierarchical func-tion which uses pairwise comparison of AHP. The resulting values of actual performance are compared with the resultant value of standard passing performance for grading purpose. From the passing grade the whole sustainability achieved will be classified into 5 grade-classes as: Gold, Silver, Bronze, Copper and Zinc. The total grade range considered is from 0 to 1. The range between passing performance and 1 is divided into 3 categories (the interval of each of these category is termed ‘Upper Interval’). The range between passing performance and 0 is divided into 2 categories (the interval of these 2 categories are termed ‘Lower Inter-val’). If the actual performance is more than the passing grade then it is agreed that the FMU is following a sustainable path with the calculated grade-class of achievement. The present research only deals with the complexity and important uncertainty traps associated with sec-ond and final processing step, which by and now have widely been dealt with Multi-Criteria Decision making methods. Precise evaluation of related data is the most crucial problem in many decision-making methods (Evangelos Triantaphyllou and Chi-Tun Lin,1995) and hence step 2 is inevitable to link the data acquisition process and in totality it determines the whole effort of the forest management unit, so care and sincerity must be advocated. Depending upon the grade achieved by the FMU, the surveillance will be done during the coming years. When FMU gets GOLD, then in the next 5-year period there will be 2-time surveillance. If FMU gets SILVER then 3 times surveillance within 5 year, if BRONZE then 4 times surveillance will be done. By doing this, the time component of the sustainability is


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well taken into account and it helps the FMU to have unceasing efforts in maintaining the Forest Unit.

Parameter Production Principle Ecological Principle Social Principle

Weight X Y Z

Passing Performance X1 Y1 Z1

Actual Performance X2 Y2 Z2

Overall Passing Value [ X * X1 + Y * Y1 + Z * Z1 ] = P

Overall Actual Value [ X * X2 + Y * Y2 + Z * Z2 ] = Q

Upper Interval (1-P) / 3 = U

Lower Interval P / 2 = L

Ranking Ranges

Gold

(P+2U) to 1

Silver (P+U) to {(P+2U) - 0.001}

Bronze P to {(P+U) – 0.001}

Copper

L to (P - 0.001)

Zinc

0 to (L – 0.001)

Table 3.1: Final SFM Grade Making Process

3.4. Technique for Assessment: Analytical Hierarchical Process (AHP)

The MCDM technique used for the final integration of all available observations is through Analytical Hierarchical Process (AHP). Since we will be comparing the results from other methods with the results of AHP it is very important to introduce the new-readers to the ba-sics of AHP. AHP was introduced by Saaty (1977,1980) which has the basic assumption that it is always easy to compare two things at a time. Here the alternatives in hand are compared with one another with reference to achieving the given criteria. These comparisons amongst alternatives are called Pairwise Comparison. This approach has provided 9 range verbal scale like Equally important, Weakly or Strongly important. These verbal scales are entered in terms of numbers from 1 to 9 in the pairwise comparison matrix. The same numbers are en-tered as reciprocals if the comparison elements are opposite nature. The scale is given in Ta-ble 3.2. So by such comparison user can make a pairwise comparison matrix. It is very much

Gold

Silver

Bronze

Copper Zinc

P

0

1

L

U


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possible that when providing this comparison value user may specify wrongly/inconsistently like saying A is “strongly preferred” than B, B is “Moderately Preferred” than C and C is “Strongly preferred” than A. When A is better than B and B is better than C, C cannot be bet-ter than A. This is called “Inconsistency”. Such inconsistencies can be checked mathemati-cally. But it is also important to note here that manipulating the preference values just to get consistency will not reflect the true final decision.

Intensity of Scale Meaning

1 Equally preferred

3 Weakly preferred

5 Moderately preferred

7 Strongly preferred

9 Absolutely preferred

2,4,6,8 Respective intermediate preferences

Table 3.2: AHP Comparison Scale

Very first step before using AHP is that the problem in hand must have the alternatives, which are comparable in nature. But Sustainability measurement embeds different disciplines and hence different parameters, so we have to break down the problem into hierarchically smaller parts, starting from the objective to criteria to sub criteria down to the verifier level in order to make them comparable. Then pairwise comparison of different criterions/alternatives to pro-vide the relative importance value between two alternatives/criteria is done at each level. In the present LEI system (Figure 3.2), we have different levels (Principle, Criteria & Indica-tors) and at the bottom most level we have 5 alternatives for every indicator: Excellent, Good, Fair, Poor, Bad. Expert Panel II members are asked to provide pairwise comparison matrix involving all these 5 alternatives in terms of achieving the corresponding Indicator perform-ance as needed for Sustainable management. This is done for all the indicators available. Then these pairwise comparison matrices are analysed to find the performance ratings of each of these alternatives in achieving the related indicator. Then the individual absolute perform-ance ratings have to be normalised by dividing them by the maximum, so that we get a feeling of relative performance values of each of these alternatives. There are 2 main reasons for normalisation. First reason is to make visible the clarity in performances between the alternatives within a single indicator and second reason is to bring all the indicators to the same platform, so that their values are comparable and aggregatable. Similar process is done for all the hierarchical levels. In bottom most level alternatives are compared with each other with respect to Indicators, this will give the performance ratings. In the next level Indicators are compared with each other in achieving the Criteria, this will give the weights for Indicators. Next Criteria are compared with one another in order to achieve


17

Principle; this will give the weights for criteria. Finally Principles are compared with each other in achieving Objective, to get the weights of principles. Except the bottom level all the comparison done at top levels produces the weights and these weights are shared downwards till bottom level during aggregation. Now we have to provide input values for representing performances of each Indicator. The Expert Panel II does this. They will specify (chose) the “Actual Performance” value and “Standard Performance needed to get Passing Grade” value for every indicator from the cal-culated performance ratings available for each indicator. So finally we will have 2 effective alternatives performance values. These values will be hierarchically integrated by just multi-plying by weights and adding them together till the top most level (weighted sum). The final single value for both the alternatives will be transformed into “Grades” as specified in the Table 3.1. For the present research only top 6 indicators (P1.1 to P1.6) leading to Forest Resources Sus-tainability are considered in order to develop a fuzzy based methodology. Figure 3.4 repre-sents the part of Certification Scheme (& their descriptions) used in this research. In the cho-sen hierarchy the Criteria Area Management (AM) part deals with the basic pre-requisites needed to keep the forest secured. In this part for 4 Indicators, 13 verifiers are chosen by the expert. Another Criteria, Forest Management (FM) deals with the core activities related to Production aspects and here 2 indicators having 5 verifiers are considered as major elements. Finally these two criteria leads to Principle, Sustainability of forest Resources which ensures the long term stability and security of natural production forest. Appendix A-I & A-II gives the complete original description given by LEI about the Indicators and associated Verifiers.


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Figure 3.2: Hierarchical Framework of SNPFM

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Figure 3.3 : Certification Process in Indonesian Scheme

(Adopted from Emil Salim et al. 1997)


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Q u a ra n te e o fL a n d U til is a io na s F o re s t A re a

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Figure 3.4: The portion of SFM hierarchy chosen for the present study


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4. Chapter IV: Methodology

4.1. Framework of decision processes

Remote Sensing and GIS have provided an efficient way for mapping, analysing and monitor-ing the ground reality at varying spatial and temporal scales. The final derivative of these technological innovations is a map, which shows, quantifies the problem area and its spatial patterns. No doubt that maps have been a key element for passing on information at different decision levels. But the problems associated with the human-nature interactions are complex and it involves multiple objectives. This multiple objective problem, ranges from human rights to environmental rights, is an integrated domain called “Sustainable Development” and cannot be quantified/mapped by a single criteria or indicator or verifier or by single domain. Hence multiple criteria are needed and different policy option has to be tested for its impact over various domains by analysing these criteria. In any planning and decision making process, a systematic and logical approach is put into operation to arrive at the solution. This systematic process can be broadly divided into 4 ma-jor phases as intelligence, design, choice, and finally implementation as an add-on phase to achieve the decision in reality. Intelligence phase deals with the problem identification, classi-fication and decomposition. Generating, developing and analyzing possible courses of action for the problem situation are dealt in Design phase. Search, evaluation and recommending appropriate solution is done at choice phase (Efriam Turban 1993, Sharifi & Marjan 2002).

4.1.1. Non-spatial decision path

Conventionally multi-criteria decision problems are used to identify the best alternative from a set of qualified inputs. This is represented by means of effect table. In the effect table, Crite-ria and Alternatives are arranged as columns and rows or vice-versa (Fig.4.1). Criteria are the characteristic quality of these alternatives. Usually this matrix contains crisp numerical val-ues for each intersection point of Criterion and alternative representing the performance value of that alternative with respect to that particular criterion. Performance values come from ei-ther the qualitative evidence of an expert or from a quantitative measurement or a quantitative fact. So the effect table is a 2-dimentional, non-spatial array of elements. Once the effect table is filled up, best alternative can be selected by comparing the performances of each al-ternative with respect to other for all the criteria. Apart from the performance value assign-ment, different criteria can be looked as different order of importance in the decision-making. In such cases Decision maker can give his priorities as weightages.


22

In reality, the ground processes cannot be quantified by a single value, because the spatial interactions over neighbouring elements are different at different locations. Hence environ-mental problems have extra characteristics, which concern the available information, expected effects and the decision environment (Janssen, 1992). Hence the consideration of spatial in-formation and the associated characteristics are important in the environmental decision proc-ess.

4.1.2. Spatial decision path

In the spatial decision-making, the crisp non-spatial performance value of the effect table has to be replaced by a spatial map. Thus the effect table now becomes 4-dimensional and can be called “Spatial Effect Table” (SET) (Fig. 4.2). Before analysing this “spatial effect table”, it must be clear that whether the role of space is useful or not to the problem in hand. Marjan (1999) have categorised this spatial character into 3 types as: Explicitly Spatial, Implicitly Spatial and Non-Spatial. Explicitly Spatial refers to the fact that the importance/impact of per-formance of an alternative over various zones are to be considered differently and hence it cannot be converted into a single quantitative value. For example, forest fire at the valuable wooded area and near human settlement is more worrisome than the forest fire over a bush wasteland. Implicitly Spatial refers to the phenomenon which can be derived from a spatial information, but the performance value over different region is equally important for example within a single forest management unit of same forest type class, occurrence of forest fire at different location is equally affecting the harvesting plan, in such case total area affected by fire can be a single quantitative information needed rather than over different region. In the final category of Non-Spatial, spatial dimension is either not at all necessary or entirely lack-ing for example total population. Once the spatial effect table, spatial category and decision priorities are set, we have to move further to analyse the SET. In most of the decision related problem, the data in hand are het-erogeneous and hence we have to have clear view of how these diverse data can be integrated. There are 3 ways by which we can integrate these diverse data Figure 4.3. Marjan (1999) have considered only first 2 paths for converting spatial effect table. Path 1 first converts all the spatial element into non-spatial element through ranking or rating or using different ad-vanced aggregation techniques like “Contagion Index”, “Fragmentation Index” and

Alternative - 1

Criteria - 1 Criteria - 2 Criteria - 3 Criteria - 4

Alternative - 2

Alternative - 3

Alternative - 4 Figure 4.1: Non-Spatial Effect Table


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Indicator - 1

Indicator - 2

Indicator - 3

Indicator - 4

Integrate Spatial mapalong each Indicator

PATH 2

PATH 3

MODEL

(ANY Level)

MODEL

Indicator - 1

Verifier - 1 Verifier - 2 Verifier - 3 Verifier - 4

Indicator - 2

Indicator - 3

Indicator - 4


PATH 1

Integrated value MODEL

(Verifier Level)

(Indicator Level)

Indicator - 1

Indicator - 2

Indicator - 3

Indicator - 4


PATH 2Indicator - 1

Indicator - 2

Indicator - 3

Indicator - 4


PATH 2

PATH 3

MODEL

(ANY Level)

PATH 3

MODEL

PATH 3

MODEL

(ANY Level)

MODEL

Indicator - 1


Indicator - 2

Indicator - 3

Indicator - 4


PATH 1


(Verifier Level)

(Indicator Level)

MODEL

Indicator - 1


Indicator - 2

Indicator - 3

Indicator - 4


PATH 1


(Verifier Level)

(Indicator Level)

Figure 4.3: Integrating Paths for Heterogeneous data

Alternative - 1

Criteria - 1 Criteria - 2 Criteria - 3 Criteria - 4

Alternative - 2

Alternative - 3

Alternative - 4

Figure 4.2: Spatial Effect Table


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“Fractal Index” and integrate them using normal MCDA process or pass it to any type of model. In Path-2 every parameter is converted into spatial data and in the next step the com-posite spatial map derived through overlay analysis is aggregated to derive useful informa-tion. Path-1 is prescribed when the input parameters are either implicitly spatial or non-spatial. Path-2 is prescribed where spatial priorities play a key role partially. In some cases these two paths cannot be followed. For example, remote sensing data cannot be converted into single quantity and when spatial priorities play an important role in the final decision. In such cases Path-3 is prescribed. Here the Explicitly spatial elements are overlayed first. Once they are overlayed, in the attribute table for each polygon we will get the corresponding col-umns of each layer used for overlay. Hence each record in the table can be considered as one non-spatial quantity (though they are linked to a single polygon) and shall be passed on to a model for processing. Finally processed information can be put in the corresponding polygon record and shall be seen spatially. This way we can efficiently process ‘AS MANY LAYERS’ in the evaluation, which in other case would require huge amount of hard disk space and processing time. As said in our earlier chapters that the major problems associated in making the SET in as-sessing sustainability of forest management unit are a) the verifiers available are of both spa-tial and non-spatial type b) it involves experts knowledge c) needs inputs from different stake holders and d) needs assessment from different experts. Also there is no way we can include explicitly attitude and uncertainties involved with the decision makers in the present system of evaluation. There are 3 possible ways in which improvements can be made to the current system. First way is just include the uncertainty associated with the input and process them using any mathematical model. Second possibility is that use crisp inputs but aggregate them using ex-pert knowledge (using inference engine) and third possibility is that associate the uncertainty in the GIS integrated input and also use expert knowledge for aggregation. Figure 4.4 depicts them in a graphical manner and associated methods for each possibility. Keeping in view the above points, the current problem of measuring Sustainability in Forest Management is analysed for different new methods to propose a methodology which can best make use of available technology and can handle the problems associated effectively and effi-ciently. To cover the whole decision making process as said above, the following methods are investigated

��2-Tuple Fuzzy linguistic Approach ��Fuzzy AHP ��Fuzzy Reasoning Approach ��Cognitive Mapping Process ��Type-2 Fuzzy Logic Approach


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Qualitative / VerbalInputs

Mathematical Aggregation

Crisp Meta IndicationCrisp Values

Input Processing

Qualitative / VerbalInputs

Mathematical Aggregation

Crisp Meta IndicationCrisp Values

Input Processing

Any Mathematical ModelQualitative / Verbal

Inputs Fuzzy Values Any Mathematical ModelQualitative / Verbal

Inputs Fuzzy Values

Expert ruleQualitative / Verbal

Inputs Crisp Values Expert ruleQualitative / Verbal

Inputs Crisp Values

Expert ruleQualitative / Verbal

/GIS Inputs Fuzzy Values Expert ruleQualitative / Verbal

/GIS Inputs Fuzzy Values

2-Tuple Linguistic Appraoch (or) Fuzzy-AHP 1st Possibility

Inputs from AHP + Inference Engine 2nd Possibility

Fuzzy Reasoning (Type-1 or Type-2) 3rd Possibility

Figure 4.4: Possible Improvements to the current certification system


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4.2. 2-Tuple Fuzzy Linguistic Approach

In many MCDM approaches decision maker is able to use most of the times only quantitative values (qualitative values has to be entered as ranks or rates). But day-to-day problem in-volves both the type. The currently used AHP approach has provided a way to integrate the expert knowledge as qualitative data through simple pairwise comparison. But once Pairwise Comparison Matrices are converted into numeric values, the role of linguistic strength (Bad or Fair or Good etc) associated with each verifier/indicator is not considered during integration. The initial problem is how to integrate numeric data, qualitative data and linguistic strength during aggregation. At this juncture 2-Tuple Fuzzy linguistic Approach comes very handy. This approach uses only FUZZY MEMBERSHIP Curves to involve the fuzziness associated with the input and remaining calculations are done with respect to characteristic value approach. Here numeric data & qualitative data is converted into uniform 2 tuple data (S,α), where S is the associated linguistic class and α is the numeric strength of that class. Also in real life different experts have their strong opinion about the way they deal with the information presented to them. So satisfying/modifying their idea creates sarcastically ego problem, this problem is not usually dealt in most of the MCDM. But in this approach it is possible to use multiple fuzzy linguistic classes from multiple experts and they can provide different membership curves in the respec-tive domain and finally all can be integrated using Multi-Granularity transformation process. But in the current research Multi-Granularity transformation process is not dealt.

4.2.1. Methodology

Herrera & Martinez (1999 a, b) have proposed an aggregation model for integrating numerical and verbal information easily and without loss of information. They have given detailed ex-planation for processing and how information loss can be avoided using the fusion process using 2-tuple representation approach. First step in this approach is defining the linguistic classes and its membership functions for each criterion. Triangular Membership curves are recommended. So the linguistic term set is defined having 5 classes {Excellent, Good, Fair, Poor, and Bad}. They propose 3 conditions for the linguistic term set to obey in order to avoid the information loss.

Condition 1: The linguistic term set does fuzzy partition. Fuzzy partition means dividing the fuzzy variable space in such a way that the sum of membership values of different linguistic classes must be Unity for any input value.

Let S = { S0, S1 ,S2 S3 S4 } then Xxxn

ii ∈∀=�

=1)(

0µ Eqn. (4.2.1)

Condition 2: The membership functions of its terms are triangular. Condition 3: For every linguistic term membership function there must be only one value in the universe of discourse X for which the membership degree is 1.


27

Once the linguistic term set is defined and conditions are met (Step 1), we can obtain the input values from the user for all available alternatives with respect to all available criteria (Step 2). If the users do not have numeric values then he can specify qualitatively by just providing the Linguistic class available in the respective criteria. Now we have to convert this information

into linguistic 2-tuple using ∆&, χτ functions (Step 3) as defined below:

For Multiple inputs one has to find the aggregated performance (Step 4) value after applying

∆&, χτ functions. For this purpose one can use extended Arithmetic Mean Opera-

tor (AMO) or Weighted Average Operator (WAO) or Ordered Weighted Aggregation (OWA) operator and many more (Herrera & Martinez 1999 a). Once we have aggregated the inputs

we can again convert it into Characteristic Performance value using κδ & functions

(Step 5) as defined below

βµ

µτχ =

�=

�== n

ii

n

iii

x

0

0*

)]([ Eqn.(4.2.3)

},....2,1,0),,{()( niSx ii == µτ Eqn.(4.2.2)

)5.0,5.0[)()(

−∈−====∆

αβαββ

iroundiwhereS i Eqn.(4.2.4)

βαα =+=∆− iS i ),(1 (Eqn.4.2.5)

htrunchwhereSS hh

−===−= +

βγβγγβδ )()},(),1,{()( 1 Eqn.(4.2.6)

valuemembershipMaximumxx

FunctioValuesticCharacteritheisCVWhere

hh

SCV

SCVSCVSS

h

hh

==

+−+ +=−=

)(|)

)Eqn.(4.2.7

*))1(*)1

(

(()],(),1,[()]([1

µ

γγγγκβδκ


28

At the end we have a crisp output, using any type of input. This model can be used for any situation in any domain. No need for expert rule. No need for big calculation. This model just depends on the number & type of membership functions used. Multiple experts have com-plete freedom to provide their indigenous definitions, values for linguistic classes and per-formance values/classes for different alternatives. The major advantage of this method is able to include fuzziness and the associated linguistic class, strength with the input data. But dis-advantage is there is no explicitly way in which we can justify the weights given during ag-gregation (step 4) and its compensation.

4.3. Fuzzy AHP

In AHP, the decision maker (DM) is asked to provide relative performance of each alternative with respect to every other alternative in achieving particular criteria. This approach has been widely used due to its simple comparison approach of taking only 2 parameters at a time and ability to provide inconsistency. But this has only 9 scale crisp inputs and it highly depends upon the user judgment. Since decision maker cannot exactly specify the relative performance accurately the results always has the possibility of uncertainty. There is no way we can explic-itly include DM’s confidence and attitude in the original AHP. To incorporate DM’s uncertainty in judgment we have to use FUZZY AHP. In Fuzzy AHP, instead of single crisp value, a range of value will be used. Again, out of this range DM can pick up values as per his confidence and also one can specify his attitude like optimistic, pes-simistic or moderate. Optimistic attitude takes the highest value of the range, Pessimistic atti-tude takes the lowest value in the rage and Moderate attitude takes the middle value of the uncertain range. This approach is useful in the present context. Hepu Deng (1999) have pro-posed and shown comprehension of this approach. This approach is extended to suit for the current LEI Certification Model of multiple-Hierarchical Structure.

4.3.1. Methodology

The Fuzzy-AHP consists of 10 steps as specified below Step1 Acquisition of Normal (crisp) Pairwise Comparison Matrices (PCM) Step 2 Fuzzifying the Crisp PCM to Fuzzy PCM Step 3 Calculation of Performance ratings using Fuzzy Extent Analysis Step 4 Weightage Multiplication from Hierarchy Step 5 Embedding Uncertainty of Decision Maker (confidence) through Alpha_cut analysis Step 6 Embedding Attitude of the Decision Maker through Lambda Function Step 7 Normalising the Effect Table Step 8 Positive & Negative Ideal Similarity Vector Identification Step 9 Similarity measurement using Vector Matching Function Step 10 Final Performance Index Measurement The fuzzification function used by Hepu Deng (1999) has some drawbacks and hence it is modified. Detailed Modified Methodology with equations and figures are explained clearly in the Appendix C-I for the ordinary user to follow the research.


29

4.3.2. Extension to suit LEI System

In the view of current research, the above methodology has to be extended little bit. In LEI certification process we have only 2 alternatives (one is the “Actual” performance and another one is the “Passing” performance), but there are multiple levels. For the current research only the level below Forest Resources Sustainability (FRS) is considered. Under this FRS, we have 2 criteria: Area Management (AM) and Forest Management (FM). Under AM we have 4 indi-cators (P1.1, P1.2, P1.3 & P1.4) and under FM we have 2 indicators (P1.5 & P1.6) (Figure 3.4). Each indicator has 5 alternatives Excellent, Good, Fair, Poor and Bad. We start from the top level. Here First of all we have to provide pairwise comparison (PCM) of AM and FM in achieving FRS. Second we have to provide a PCM comparing indicators among themselves so one each for AM and FM. Now we got 3 PCMs. Next providing PCM among alternatives for achieving each indicator. Here under AM, we will get 4 PCM and under FM we will get 2 PCM. So in total we have 9 PCM. From the available PCM, first we will do steps 1 to 3. Now we will have performance ratings and weightages at different levels. Now we have to share these weightages of top level to bot-tom level, so we will just multiply the fuzzy weights obtained at FRS with fuzzy weights ob-tained at one level below it (i.e., AM/FM level). Now again these weights are shared with one more level down under respective criteria (i.e., Indicator level). Hence finally we will have single overall weights and one performance matrix for AM and FM respectively. Now for each indicator we will have possible performance ratings for Excellent, Good, Fair, Poor and Bad. Now DM will be prompted to select any value while keeping view the “current Actual performance of the FMU” in relation to that indicator. This will act as one alternative. Next DM has to again choose the performance ratings for “Passing performance needed to qualify”. This will act as second alternative. Now we have combined different hierarchical structure into a single level effect table consists of alternatives and integrated weights. Now we will follow the remaining steps 4 to 10, to identify the final performance index (FPI). If the FPI value of current performance is more than the standard one, then the FMU is considered to be performing better and as per the pro-cedure described in Table 3.1, the respective Label will be given after necessary fulfilment.

4.3.3. Advantage of this Process

��This approach can incorporate Uncertainty and Attitude of the Decision Maker. ��This provides an option to analyse the impact of different scenarios on the final rank-

ing or rank reversal process. ��Mathematically easy to calculate all the fuzzy extension. ��It inherits strong conceptual theories from multiple approaches.


30

4.4. Fuzzy Reasoning Approach

Whenever the complexity of the system increases, the accuracy of measuring, interpreting and identifying its behaviour becomes more and more difficult. After certain threshold the sys-tems just get merged as amalgamation of multiple domain, which in turn have their own com-plex interaction in itself. Human intelligence is one of such most complex system, next comes Environmental interactions. Evaluating such system with crisp numerical approach would not represent or lead us to reality. In such cases Fuzzy logic concepts comes handy.

4.4.1. Linguistic Variable, Linguistic Classes and Fuzzy set

Any variable which has many interpretational possibilities can be thought as fuzzy variable or linguistic variable. Main role of linguistic variable is to provide a way of working with com-plex system. When we try to represent such a variable in terms of human language, then it leads to “linguistic classes”. Speed and temperature though can be measured, can be thought as linguistic variables and the interpretation of that variable in human words like super fast, Very fast, slow, somewhat fast, very cold, very warm, can be thought as linguistic classes. Normally linguistic variables are not exactly measurable and may be categorized into any one of the linguistic classes, hence linguistic variable can also be called fuzzy variable. A set whose members are fuzzy variables or linguistic variables can be considered as fuzzy set and its Universe of discourse contains all the objects of particular kind. Fuzzy set allows the par-tial membership of elements. Membership refers to the degree of belonging to a particular class. In the present context all the verifiers, Indicators, Criteria and Principle are considered as linguistic variables and each of them have their respective linguistic classes from the group {Excellent, Good, Fair, Poor and Bad}.

4.4.2. Measurement & Standardisation Process

One of the major problem in the current forest certification process is that most of the verifi-ers are implicitly spatial, their measurement are vaguely defined and most of them are ver-bally assessed through experts judgment (Appendix A-I showing indicator-verifier meaning table). Assessment team just check the ground reality with respect to spatial plan maps and verbally describes the total condition of the management unit in the report. Since most of the information is non-spatial and implicitly spatial, the small number of existing spatial elements is also needed to be converted into a crisp quantitative value in order to follow the path-1. To integrate such elements logical aggregation procedure using GIS is needed. Figure 4.6 pro-vides a procedure to aggregate spatial elements associated with Indicator P1.2 (Forest Plan-ning & Use). Appendix A-II exemplifies the verifiers considered by the Experts during evaluation, their possible way of measurement & standardisation procedure. Since different verifiers are measured in different unit all the verifier’s values have to be stan-dardised to a common scale in order to allow fuzzy calculations. Standardization of verifiers will be done individually with reference to its own available minimum, maximum possible values and user preferred value of that verifier in the view of satisfying sustainability. The


31

standardized values will be seen in terms of linguistic classes, which will have to be applica-ble uniformly to all the verifiers. Example of standardisation curve is shown in Figure 4.5.

It is very important to note here that depending upon the nature of the verifier like whether it is ‘COST: less the better’ or ‘BENEFIT: more the better’, user has to choose the standardisa-tion curve accordingly. For COST verifier normally curve should have decreasing slope and for BENEFIT the curve will have increasing slope. Also in some cases moderate values are needed and in such cases triangular or trapezoidal shaped curves would be helpful. Since the verifier can take any value over its measurement domain, the endpoints can have open curve, means beyond/below certain value the curve will take single value. By this standardisation procedure all the verifiers value will be transformed between 0 and 1. Appendix A-II tries to show the procedure to do standardisation for different verifiers. It is very much possible to feed the raw values of verifiers directly onto the FUZZY MODEL, but in that case user has to define for each verifier the different shape of membership curve and over different range of original domain values of the verifier. This process involves tre-mendous amount of uncertainty in defining linguistic classes directly from the raw values. The big advantage of doing/defining standardisation curve beforehand lies in reducing such uncertainties.

Verifier ‘J’ Unit “xx”Verifier ‘J’ Unit “xx”

Figure 4.5: Standardisation possibility for verifiers


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Figure 4.6: Spatial Aggregation Pro-cedure for the Verifiers involved in Indicator P 1.2 (Forest Use & Plan)


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4.4.3. Fuzzy Membership function and its interpretation

Membership function maps the variation of value of linguistic variables into different linguis-tic classes. The adaptation of membership function for a given linguistic variable under a given situation are done through 4 ways: a) experts previous knowledge about the linguistic variable b) using simple geometric forms having slopes (triangular, trapezoidal or s-functions) as per the nature of the variable and c) by trial and error learning process. An important point to mention here is that the shape of the membership curve also reveals the uncertainty/confidence involved in allocating a value to particular class. Triangular member-ship curves with moderate slope reveal that the DM is uncertain about the highest degree of membership (HDOM), also he is not confident about its range. Triangular membership curve with steep slope has uncertainty about the highest degree, but decision maker is confident about its range. Trapezoidal curves reveals that DM is very confident about HDOM at the middle range, but has uncertainty only at the edges of each class. Gaussian curve is consid-ered to be representing more moderate DM than triangular one. Since LEI system has 3 hierarchical levels, membership functions for linguistic classes of each level is to be defined. Number of linguistic classes and corresponding membership func-tions will be selected after a discussion with the authorities and experts related with study area. Without expert’s experience choosing membership function will be very subjective, dif-ficult and it would only reflect the lack of understanding of decision approach on the problem. In the present study only expert’s opinion is utilized in making the membership function and selecting the shape of the membership curve.

Triangular membership curves are considered by many of the experts during the field visit. In the LEI system, the number of linguistic classes chosen at the verifier level are 3. Excellent, Fair, Bad. Number of linguistic classes at Indicator level are 5 as Excellent, Good, Fair, Poor & Bad and Finally number of linguistic classes at Principle level are also 5 but considered as

Deg

ree

of m

embe

rshi

p

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

Indicators

Bad Poor Fair Good Excellent

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

Indicators

Bad Poor Fair Good Excellent

Figure 4.7: Fuzzy Linguistic Classes & Membership curves


34

direct certification labels like Gold, Silver, Bronze, Copper & Zinc. Example Membership classes and associated functions assigned for Indicator level is shown in Figure 4.7.

4.4.4. Knowledge Building

In the Fuzzy Reasoning Model, expert’s knowledge is needed at different levels. At the base level it helps in making the “Causal Relationship Diagram”, at the mid level in choosing stan-dardisation curve, selecting number of linguistic classes & shape of the membership curves and at the Core level his experience in judging the interactions is needed as “RULES” for fuzzy inferencing. Hence much care, attention and patience has to be given in acquiring their knowledge in breadth and depth.

4.4.5. Expert Rule Acquisition

A time taking and very important part of this approach lies in building the Rule-base. For every Indicator, Criteria and Principle we have to acquire rules. Number of rules depends on number of inputs (linguistic variables) and number linguistic classes of the inputs. For exam-ple the Indicator P1.1 (Guarantee of Land Utilisation as Forest Area) has 3 verifiers. These verifiers have 3 linguistic classes each, hence total number rules required to get the inference of Indicator P1.1 is 3*3*3 = 27 rules. Indicator P1.3 (Forest Change) has 4 verifiers in that case number of rules becomes 81, but in reality one can easily optimise and reduce the num-ber of rules. Appendix E completely represents the optimised rule diagram as Decision Tree for all the indicators (P1.1 to P1.6), Criteria & Principle. While building the rule-base it is very important to note down the arguments used by the ex-pert for giving that rule-result. It would be impossible to get the arguments for all the rules due to huge amount of inputs and also non-availability of his time, but the major backbone arguments, which keep the logic consistent, must be written down with his concurrence. The following paragraphs depict the major arguments used for building the rules (Haryanto et al. 2002) for the current research. The reader is requested to look Appendix A-II to know before hand the different verifiers chosen by expert for different indicators, in order to follow the below discussions. 4.4.5.1 Indicator P1.1 (Guarantee of Land Utilisation as Forest Area) Here the verifier “Stake holders agreement” is considered as most important, next “legal ful-filment” and last “Boundary demarcation & implementation”. If stakeholder’s agreement is bad then everything goes bad. Stake Holders agreement also plays a role in modifying legal fulfilment. Meaning that if stake holder’s agreement is good then possibility of legal fulfil-ment getting ‘bad’ is low. But reverse is not true, means that legal fulfilment may be good but it does not mean that stakeholder’s agreement will be good.


35

4.4.5.2 Indicator P1.2 (Forest Planning & Use) Here the first two verifiers (Production & Protected area plan as per Land capability and as per Forest Classes) be related to “planning map” are considered equally important and next is the “implementation of Production & Protected area Plan” verifier. If the any one of the plans is bad, then implementation cannot be good and if both the plans are good then implementa-tion may be good or may be bad. 4.4.5.3 Indicator P1.3 (Forest Change) Here the verifier “Intensity of Forest Fire” is considered to be most important at the first place. Second comes “Forest Encroachment” and third comes “Other disturbances” and “Overcutting”. If the intensity of forest fire is very high then output is Bad and it overrules every other good performance. If the verifiers are moderate or low then output may be com-pensatable depends on other verifiers performance. Since this indicator is the Cost indicator: Lower the better, we have to give extra care in understanding this otherwise it will lead to compensation, which is not we wanted and not possible in nature. 4.4.5.4 Indicator P1.4 (Level of Early Warning System) This Indicator depends on the verifiers “Early Warning System”, “Community & Institutional Participation” and “Availability Skilled Labours, standard procedure”. If the Early Warning System is bad it means that pre-caution measures are not taken by the forest management and it leads to the believe that “if they are not prepared then they cannot fight fire at the early stage”, so every effort goes Bad. Other two verifiers can compensate for each other. 4.4.5.5 Indicator P1.5 (Silviculture Plan & Implementation) Here Implementation of Silviculture Practices is considered as most important and Compli-ance with local eco system at the second importance and remaining are considered equally together at last. Here again good Implementation implies the good compliance with local eco-system and it overrides all other lower performances. Moderate implementation can be compensated with other good performances. 4.4.5.6 Indicator P1.6 (Sustainable use of NTFP) Here the verifier “Availability of different Types of Non-Timber Forest Products’ is consid-ered first important, because if the forest management do not know this then they cannot find out other verifier “potential extractions of NTFP”. Both the verifiers are needed to have good performance. 4.4.5.7 Criteria: Area Management (AM) (Basic Requirements of FMU) In the second hierarchical level from the bottom, the criteria Area Management comes which envelopes Indicators P1.1 to P1.4. Since We have 5 linguistic classes for each of the input total rules required here is 5*5*5*5 = 625 rules. Here Indicator P1.3 is considered as the first


36

important, second is P1.1, third is P1.2 and last is P1.4. Again If P1.3 is bad, which implies that Intensity of Forest Fire is very high it overrides all other indicators good performance. Extreme performances are not compensatable. It is also important to note here that output per-formance cannot be better than the performances of P1.3 & P1.1. Other two verifiers can be compensated. 4.4.5.8 Criteria: Forest Management (FM) (Core Activities of FMU) The criteria FM envelops indicators P1.5 & P1.6. Out of these two P1.5 is considered first and P1.6 as second important. Again P1.5 dominantly controls the output performance in the extreme cases and in the moderate one it is little compensatable only in pulling lower degree not in pushing toward upper degree. 4.4.5.9. Principle: Forest Resources Sustainability (FRS) The third level parameter is Forest Resources Sustainability Principle, which has 2 inputs AM and FM. Depends on the current Typology in hand the importance of AM & FM may vary. In the current study AM is considered to be first important. Here the extreme performance of AM dominates the output and medium performance compensates the lower degree of second one. Appendix D & E describes the basic Fuzzy Set Theory, Fuzzy Logic and the expert rules used in the present research in a clear manner. Figure 4.8 shows the conceptual skeleton of the processes involved and Figure 4.9 shows the step-by-step architecture of the Fuzzy-reasoning model proposed and its implemented model is shown in Figure 4.10


37

Measurement Domain,Meaning, Standardisation

Linguistic Variable, Classes(Input and output)

Verifiers

Identify

Define

Tier 1

Tier 2

Membership FunctionDefineTier 3

FuzzificationTier 4 Compute

Rule Implication, fuzzy integrationTier 5 Infer

Defuzzification Tier 6 Transform

Indicators& Criteria

Principle

Sustainability

Measurement Domain,Meaning, Standardisation

Linguistic Variable, Classes(Input and output)

Verifiers

Identify

Define

Tier 1

Tier 2

Membership FunctionDefineTier 3

FuzzificationTier 4 Compute

Rule Implication, fuzzy integrationTier 5 Infer

Defuzzification Tier 6 Transform

Indicators& Criteria

Principle

Sustainability

Figure 4.9 : Architecture of Fuzzy Reasoning Model

Verifiers

Indicators

Criteria

Principle

stake holder1 stake holder2stake holder n

extreme value definition

standardisation definition

target range definition

membership function definition

inference rule generation

fuzzy connectives selection

Expert 1 Expert 2Expert n

LEVEL OFSUSTAINABILITY

inference engine

Sustainability Hierarchy

Inference Engine

Compilation

Defuzzification

Verifiers

Indicators

Criteria

Principle










Verifiers

Indicators

Criteria

Principle

VerifiersVerifiers

Indicators

Criteria

Principle











Integration technique selection




knowledge base

Compilation

Defuzzification

Verifiers

Indicators

Criteria

Principle










Verifiers

Indicators

Criteria

Principle

VerifiersVerifiers

Indicators

Criteria

Principle














inference engine


Inference Engine

Compilation

Defuzzification

Verifiers

Indicators

Criteria

Principle

VerifiersVerifiers

Indicators

Criteria

Principle














VerifiersVerifiers

Indicators

Criteria

Principle

VerifiersVerifiers

Indicators

Criteria

Principle















knowledge base

Compilation

Defuzzification













knowledge base

Compilation

Defuzzification

Figure 4.8: Conceptual Skeleton of the research approach


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Indicator P 1.3

Indicator P 1.1

Indicator P 1.2

Indicator P 1.4

Indicator P 1.5

Indicator P 1.6

Forest Encroachment

Intensity of Forest Fire

Other Disturbances

Overcutting

Stake Holders Agreement

Legal Fulfillment

Boundary Demark & Impl.

Plan as per Land Capability

Plan as per Forest Types

Implementation

Early Warning System

Skilled Labours

Community & Insti. Participation

Silviculture Implementation

Ecosystem Compliance

St. struc, Spec.comp. Tree Regen.

Types of NTFP

Potential Extraction

Area Management (AM)

Forest Management (FM)

Forest Resources Sustainability

Figure 4.10: Implemented Fuzzy Reasoning Model


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4.4.6 Role of AHP in Fuzzy Reasoning Model

In the AHP, though there is a possibility of comparison between parameters, the missing links are ability to incorporate uncertainty in the judgement and attitude of decision maker. Also it is considered in numerical domain (converted from verbal judgements) and hence it is purely a play of numbers, which inherits compensation behaviour, means the best performance of one alternative for one criterion can compensate the worst performance for other criteria. But the environmental processes are not reimbursable, which means that when the intensity of forest fire is maximum, the loss is maximum which cannot be compensated with the higher values of “protection and production forest planning” or “Early Warning System” indicators. Also human mind efficiently analyse the things linguistically rather than through numbers. Hence we have to provide a possibility of linguistic conversion from the numerical values. Hence we need to incorporate the Experts knowledge who through their experience inferences the condition while integrating different information. This inter relationship of linguistic knowledge has to be incorporated if we want to make the system highly diligent. In this view the Aggregation part of AHP can be replaced with the Fuzzy Reasoning Model (FRM). In this case, Input to the FRM comes from the Pairwise Comparison Matrix rather than from field measurement or through RS, GIS analysis. These values will be processed to utilise the knowledge inside fuzzy reasoning model.

4.5. Cognitive Mapping Process

In the LEI certification model, different parameters have been arranged in different hierarchi-cal level and in sub-branches, which is due to the assumptions that those parameters only have potential interaction at that branch of the model. But in reality it is not true, because in the environmental phenomenon the dynamic behaviour have much wider impact and hence this assumption restricts in incorporating/mapping the real contribution of the parameters over different branch of the model. To remove this constraint, an overall interaction dynamic be-haviour / relationship has to be mapped. At this juncture, Cognitive Science has provided a way to achieve this through a process called COGNITIVE MAPPING (Eden & Akermann, 1998). Tolman (1948) first coined this term “cognitive map” in his study about identifying the memory behaviour of rats in reaching the food. Cognitive Map does not refer to any hard copy map, but it refers to “Map in the Mind” of any living being. Mendoza and Prabhu (2002) have effectively utilised this approach in evaluating the indicators of forest resources management. Very importantly, when we acquire expert rules and priorities of different parameters we have to be sure that Expert is consistent about his views. The problem in hand is how to check?. In this point of view we can obtain the “Causal Relation Diagram” (CRD) from the same expert after obtaining his rules and priorities. Now using cognitive mapping process we can get the importance order, interrelationship and many derivatives. Now we can check the one to one correspondence between the RULES & PRIORITIES derived from him and from the Cogni-


40

tive map. Also Cognitive Map can be used in a reverse manner that first define the CRD and find the interactions and accordingly define the RULES.

4.5.1. Methodology

In the Cognitive Mapping, different parameters of a process are arranged with a CAUSE-EFFECT relationship. Every parameter is connected to another parameter if it affects or it gets affected. If a parameter (say A) affects another parameter (say B) then the arrow starts from A and ends at B. If a parameter (say A) is affected by another parameter (say C) then arrow starts from C and ends at A. In short, Tail of the arrow shows the Cause point and Head of the arrow shows the Effect point. If we start building this relationship ship till it covers all the parameters, finally it will give us a complex “Causal Relation Diagram” (CRD), then we can say that we have done “cognitive mapping”. From this CRD following parameters can be derived. For every parameter (verifier/indicator) we can identify

• Direct Force (called Domain refers to number of first level interaction by or to that parameter)

• Mean Force (called Centrality refers to overall interaction in the whole process) • Forward Routes (number of possible routes a parameter is part of, by which it makes

a chain of bond in affecting others) • Backward Routes (participation in number of possible routes in which it is affected

by other chained links) It is a logical thinking that any parameter is affected more by a first level interaction than the second and higher-level interactions. Hence the Mean Force or Central Force can be calcu-lated by the following formula

4.5.2. Advantages of this Process

• From this process we can understand which parameter is playing a Major Role in af-

fecting the whole process and we can put all these parameters in an ascending order for the purpose of prioritising.

• We can also find out whether a parameter is a Pressure variable or Response variable

or both. Pressure variable is the one which affects other and Response variable is the one which gets affected by others.

First level interaction + 2nd level interaction + 3rd level + 4th +……+ nth

Mean Force = -------------------------- ----------------------- ----------- ---- ----- 1 2 3 4 n


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• We can also provide/deduce weights as per their overall significance

• We can also find out the Weakest Link in the process

• We can also find out Most Critical Parameter out of identified group of critical pa-

rameters. Critical parameters are the parameters whose average scores, derived from ranking process, are less than a particular value identified by experts (Mendoza and Prabhu, 2002). Most critical parameter is the one which has less average score than expert specified and also it is taking part in maximum number of Forward and Back-ward Routes.

• Last but not the least, it helps to check the consistency of the decision maker or expert

‘s views with respect to his rules.

It is evident that the Cognitive Mapping approach can play an important role in understanding the overall relationship of all existing parameters. The derivatives of this approach will help to structure the certification system effectively and efficiently and will provide a good base for final evaluation process.

4.5.3. Future Extensions

Another possibility is that CRD for all the parameters with respect to current typology can be made initially. This CRD can be considered as a BASE MODEL. Since certification assess-ment is to be done over different time period, current assessment CRD can be made and shall be compared with CRD BASE. This will reveal the change in interaction elements and we can prioritise the element accordingly. In the CRD it is assumed that strength of CAUSE and EF-FECT for every parameter is same, but in reality different parameters impact different other parameters in a different manner. Some may have higher impact than others, in such case every ARROW must consists of impact strength like positively affects, negatively affects, little, highly, very highly, etc. Then this linguistic strength is also to be included in all the pa-rameters calculations. This part can be considered for future developments in this line.

4.6. Type-2 Fuzzy Logic Approach

In most of the fuzzy applications it is being assumed that once the linguistic variable and classes are defined as fuzzy sets then uncertainty is covered. Defining a fuzzy set with just single membership function for every linguistic class implies that Decision maker is sure about variations of his real world values and its associated degree of membership values. But in reality this is not the case. Decision maker does not know the exact inter and intra class boundaries for interpretation. Hence the membership curve itself is uncertain. If we include our uncertainty about this membership curve then it becomes Type-2 fuzzy logic system. The single membership fuzzy system is called Type-1 Fuzzy logic system. There are two steps by


42

which we can include uncertainty onto type-1 fuzzy set. First is to embed uncertainty in the BASE VALUEs of the membership curve, means that the real fuzzy set may be assumed to cover lesser range of values than what we have taken or it may cover Higher range of values than what we have taken (we have to consider both the parts, called Foot Print of Uncer-tainty). Second, we can include our confidence about its associated membership value as a third dimensional height value. Computationally this method is intensive and hence one can consider Interval Type-2 Fuzzy logic approach, where the uncertainty about its membership values are assumed to be same for both the Foot print of Uncertainty. Though Professor Lotfi A. Zadeh (1975) first coined the term type-2 fuzzy logic and used by few others in late 1970s, the paramount effort put on by Professor Jerry M. Mendel (2001) and his students Dr. Nilesh Karnik, Dr. Qilian Liang (1998,1999) have really made type-2 fuzzy logic system usable to many other applications involving uncertainty inside fuzzy logic system. The present research is first of its kind in utilising type-2 fuzzy logic system to incor-porate uncertainties in the fuzzy evaluation of sustainability of forest management. In order to understand the role of type-2 fuzzy logic in the present research, it is inevitable to get good hold about components and terminologies used in Type-2 Fuzzy logic system. The terminol-ogies understood from Mendel (2001) are explained in Appendix-F in order to make the fu-ture user eligible to follow the research. Equations are adopted from Mendel (2001), some symbols may be different due to limitation in representation.


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5. Chapter V:

Analysis, Results & Discussion

5.1. Analytical Hierarchical Process (AHP) Evaluation

In order to compare, find the applicability, efficiency and effectiveness of different ap-proaches, 4 set of test data (4 different concession locations; Site1, Site2, Site3 & Site4 within study area)* were obtained from the Experts of Lembaga Ecolabel Institute (LEI), Bogor, In-donesia. Each set contains the numerical value and associated linguistic class referring the respective indicators under Expected Passing performance (minimum performance required to qualify for certification) and Actual performance (performance observed on the ground). These values are derived after processing the Pairwise Comparison Matrix provided by the experts for each Indicator (Appendix B). For each indicator, the pairwise comparison matrix was provided by experts and corresponding consistency was checked. 10% inconsistency is kept as tolerable amount, beyond which user has to modify his Pairwise Comparison matrix. Once the consistent PCM is obtained, the performance values of each indicator were obtained and aggregation using weighted sum over hierarchy was done.

The Table 5.1 Provides the ‘actual’ and ‘passing’ performance of test sites data over different indicators, which are as specified by the Expert. These values are integrated as weighted sum at each hierarchical level and the results are graded as per the definition given in the Chapter 3

(Table 3.1).

* � Since the sites are under evaluation, their confidentiality restrict me not to pinpoint in the map

AREA MANAGEMENT (AM) FOREST MANAGEMENT

(FM) P1.1 P1.2 P.13 P1.4 P1.5 P1.6 FOR SITE 1 ACTUAL 0.1894 (P) 0.7025 (G) 0.6032 (F) 1 (F) 1(F) 1(F) PASSING 0.5(F) 0.3321(F) 0.6032(F) 1(P) 1(F) 1(F)

FOR SITE 2 ACTUAL 0.2804(F) 0.4092(F) 0.4421 (F) 1(G) 0.3057(F) 0.4552(F)

PASSING 0.2804(F) 0.4092(F) 0.4421 (F) 0.5868 (F) 0.3057(F) 0.4552(F) FOR SITE 3 ACTUAL 0.5724(F) 0.5 (P) 1(F) 1(B) 0.5396(P) 1(F) PASSING 0.5724(F) 0.5 (F) 0.5 (P) 1 (P) 1 (F) 0.5 (P)

FOR SITE 4 ACTUAL 1(E) 0.6408 (G) 0.4425 (F) 0.4516 (F) 0.3835 (F) 0.3719 (F)

PASSING 0.2695 (F) 0.6408 (G) 0.4425 (F) 0.4516 (F) 0.3835 (F) 0.3719 (F) Table 5.1: Actual & Passing Performance of Test Data


44

Appendix B Provides the complete pairwise comparison matrices and provides the calcula-tion of performance values, weights and consistency check from a given pairwise comparison matrix. Also, calculated performance values of all the alternatives for each indicator and weights at criteria and principle level are given. The final certification results using conven-tional AHP approach are given in Table 5.2.

5.2. 2-Tuple Fuzzy Linguistic Approach

In this approach we have used the same triangular membership function as in Fuzzy Logic Approach (triangular) (Figure 4.7). The input data are fuzzified, then using Chi, Delta func-tions they are brought into a uniform representation level as 2-tuple (S, α), which represent the linguistic class (S) the input values belongs to and closeness measure (α) towards it. These 2-tulples are integrated using arithmetic mean with equal weights & finally using δ and K function final performance values are evaluated. All the sites were evaluated using this ap-proach and the results are shown below in the Table 5.3.

ACTUAL PASSING Grade Site1 0.4994 0.4607 Bronze Site2 0.4254 0.405 Bronze Site3 0.4565 0.4778 Copper Site4 0.5057 0.4144 Bronze

Table 5.3: Performances & Grades of All sites The Step by step process involved in input preparation and final performance evaluation (of site-1 data) is shown in the Tables 5.4a,b & Table 5.5 respectively.

PERFORMANCE Upper Interval Lower Interval Grade FOR SITE 1 ACTUAL 0.6028 0.1042 0.3438 COPPER PASSING 0.6875 FOR SITE 2 ACTUAL 0.4236 0.2071 0.1893 BRONZE PASSING 0.3787 FOR SITE 3 ACTUAL 0.7359 0.0846 0.373 COPPER

PASSING 0.7461 FOR SITE 4 ACTUAL 0.5961 0.2249 0.1672 SILVER PASSING 0.3254

Table 5.2: AHP integration results of Actual & Passing Performance


45

P1.1 P1.2 P1.3 P1.4 P1.5 P1.6 Input Actual 0.1894 0.7025 0.6032 1(Fair) 1(Fair) 1(Fair) Passing 0.5 0.3321 0.6032 1(Poor) 1(Fair) 1(Fair) After Fuzzification: Membership Values (eg.,only "Actual" data)

Linguistic Class S(i) P1.1 (0.1894) P1.2 (0.7025) P1.3 (0.6032) P1.4 (1 Fair) P1.5 (1 F) P1.6 (1 F)

Bad (0) 0.2424 0 0 0 0 0 Poor(1) 0.7576 0 0 0 0 0 Fair (2) 0 0.19 0.5872 1 1 1 Good (3) 0 0.81 0.4128 0 0 0 Excellent (4) 0 0 0 0 0 0 Chi_Function(0.1894) = 0 * 0.2424 + 1*0.7576+2*0+3*0+4*0= 0.7576 Chi_Function(0.7025) = 0 * 0 + 0*0+2*0.19+3*0.81+4*0= 2.81 Chi_Function(0.6032) = 0 * 0 + 0*0+2*0.5872+3*0.4128+4*0= 2.4128 Chi_Function(1 Fair) = 0 * 0 + 1*0+2*1+3*0+4*0= 2 chi(0.1894) chi(0.7025) chi(0.6032) chi(1 Fair) chi(1F) chi(1F)

Actual 0.7576 2.81 2.4128 2 2 2 Table 5.4a : 2-Tuple Fuzzy Linguistic Approach Input Preparation (Fuzzification & chi function)

After Chi_Function actual 0.7576 2.81 2.4128 2 2 2 passing 2 1.3284 2.4128 1 2 2 Delta(0.7576)= S, Alpha where S(round(Beta)) =S(round(0.7576)) = S(1)= Poor Alpha = Beta - round(Beta) = 0.7576 - 1 = -0.2424 therefore Delta(0.7576) = Poor,-0.2424

2-tuple actual Poor, -0.2424 Good, -0.1900 Fair, 0.4128 Fair,0 Fair,0 Fair,0 (After Delta function) passing Fair,0 Poor,0.3284 Fair, 0.4128 Poor,0 Fair,0 Fair,0

Table 5.4b: 2-Tuple Fuzzy Linguistic Approach Input Preparation (Delta function)


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2-tuple Actual Poor, -0.2424 Good, -0.1900 Fair, 0.4128 Fair,0 Fair,0 Fair,0 (After Delta function) passing Fair,0 Poor,0.3284 Fair, 0.4128 Poor,0 Fair,0 Fair,0

AM_AGGREGATION = [ Inverse_Delta(poor,-0.2424) + Inv_Delta(Good,-0.19) + Inv_Delta(Fair,-0.4128)+Inv_Delta(Fair,0) ] / 4

= (0.7576+2.81+2.4128+2)/4 = 1.9951 AM_Aggregated 1.9951 FM_Aggregated 2

1.6853 2 FRS Aggregated actual 1.9975 passing 1.8426 Del(1.9975) = (S(h), (1-Gamma)), (S(h+1),Gamma) where h = Truncation(beta) S(h) = S(trunc(1.9975))= s(1) = Poor Gamma = Beta-h = 1.9975-1 = 0.9975 Del(1.9975) = (S(1),(1-0.9975)),(S(2),0.9975) = (Poor,0.0025), (Fair,0.9975) DEL FUNCTION actual (Poor, 0.0025 ) (Fair, 0.9975) passing (Poor, 0.1574) (Fair, 0.8426)

K[del(beta)] = Max[S(h)] * (1-gamma) + Max[S(h+1)] * gamma where Max[S(h)] refers to the x-value which has the highest membership in S(h) K[(poor,0.0025),(fair,0.9975)] = 0.25 * 0.0025 + 0.5*0.9975 = 0.4994 K-Function actual (0.2500 * 0.0025) + ( 0.5000 * 0.9975) passing (0.2500 * 0.1574) + (0.5000 * 0.8426) FINAL PERFORMANCE actual 0.4994 passing 0.4607

Table 5.5: 2-Tuple fuzzy Linguistic Approach Final Performance Evaluation Steps (Site-1)


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If we compare the results from this 2-tuple approach with AHP results, this approach has given different results for site-1 & site-2. This is due to the fact that we have not used any importance weights for indicators during our aggregation. Hence this approach would have given relatively similar results if we would have provided importance weights. Then again the question comes how to define the importance weight. That is only possible during the aggregation and in that case just providing fuzzification at the beginning does not provide any advantage except the fact that the input values are associated with their linguistic order, which is not considered in the Analytical Hierarchical Process. Hence this approach is not recom-mended as an advantageous one to replace the current AHP approach used by LEI certification system.

5.3. Fuzzy Analytical Hierarchical Processing (Fuzzy-AHP)

In fuzzy AHP approach input crisp pairwise comparison matrices are fuzzified using the fuzzy membership function defined in Chapter 4.3.1. These fuzzified inputs are then converted into fuzzy performance values using fuzzy extent analysis. Next the hierarchical weightages are applied over inputs. After that Decision makers confidence and his attitude are introduced using Fuzzy alpha_cut analysis and Lambda function respectively. Then the normalization is done to get the final performance values of each indicator. From this final performance vec-tor, we can compute the overall performance of ‘actual’ and ‘pass’ by using either Vector Matching Function or Ideal Position Method. Appendix C-II gives the complete step-by-step execution and results of fuzzy-AHP for Site1. Table 5.6 a, b lists the final performance of all the sites using Vector Matching function in original Fuzzy-AHP & Modified Fuzzy-AHP respectively. Table 5.7 lists the final perform-ance of all the sites using Ideal Position method. In this approach since Confidence (α) and Attitude (λ) both has the possible values of 0 to 1, there are 121 different combinations of α & λ are possible if we take 0.1 interval in both. Though all 121 different scenarios are calculated in MATLAB, but for comparison purposes only 3 extreme scenarios were considered for dis-cussion in this research. In Scenario-1, Decision Maker is not at all confident (i.e., full fuzzy triangular base is considered, which means uncertainty is maximum) about his PCM values and he is a Pessimistic person (tries to give lowest performance value). In Scenario-2, Deci-sion Maker is 50% confident about his PCM values (uncertainty is moderate) and he is a mod-erate person (tries to give in-between performance values). In Scenario-3, Decision Maker is 100% confident about his PCM values (uncertainty is nil) and he is an optimistic person (tries to give maximum performance values).


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When alpha = 0 When alpha = 0.5 When alpha = 1

& Lamda=0 & Lamda=0.5 & Lamda=1 FOR SITE 1 ACTUAL 0.49953 0.49521 0.49689

PASSING 0.50047 0.50479 0.50311

GRADE Copper Copper Copper

FOR SITE 2 ACTUAL 0.51692 0.51227 0.51485

PASSING 0.48308 0.48773 0.48515

GRADE Bronze Bronze Bronze

FOR SITE 3 ACTUAL 0.49649 0.52183 0.52703

PASSING 0.50351 0.47817 0.47297


FOR SITE 4 ACTUAL 0.53657 0.52498 0.53034

PASSING 0.46343 0.47502 0.46966


Table 5.6a: Results of FUZZY-AHP using VECTOR MATCHING FUNCTION


& Lamda=0 & Lamda=0.5 & Lamda=1 FOR SITE 1 ACTUAL 0.50285 0.49438 0.49689

PASSING 0.49715 0.50562 0.50311

GRADE Bronze Copper Copper

FOR SITE 2 ACTUAL 0.51475 0.5136 0.51485

PASSING 0.48525 0.4864 0.48515


FOR SITE 3 ACTUAL 0.52326 0.52569 0.52703

PASSING 0.47674 0.47431 0.47297


FOR SITE 4 ACTUAL 0.53379 0.52706 0.53034

PASSING 0.46621 0.47294 0.46966


Table 5.6b: Results of Modified-FUZZY-AHP using VECTOR MATCHING FUNCTION


49

It is found that (using Original Fuzzy-AHP) the Vector matching function is sensitive to input values, but the output performance difference is not significant. For example for the Site-1 (when alpha & lambda equal to 0) the overall performance of ‘Actual’ is 0.49953 and ‘Pass-ing’ is 0.50047. The difference is only 0.00094 and hence coming to conclusion based on these small different value would be fatal. Also it is found that SITE-1 & SITE-3 values have the possibility of RANK REVERSAL, because their values are so close when alpha & lambda equal to 0 and hence attention must be given to these data set before coming to any solid deci-sion. In the Modified-Fuzzy-AHP, the diagonal elements are kept as 1 even after fuzzification and possibility of getting infinity when input is 1/2 is also kept 1. The output from Modified-Fuzzy-AHP has enhanced the difference in the output, especially in the case of SITE-2 & SITE-4 where most of the inputs are having same performance except 1 indicator. Also the modification has shown that there is a rank reversal for Site-1 when alpha & lambda are 0, which was not highlighted in original fuzzy-ahp. Also when alpha & lambda are 1, the output from both the method remains same. In Ideal Position approach, though the difference in performance values is significant, this ap-proach is not sensitive to small variation in input parameters. Table 5.7 shows the results of Ideal Position method within original Fuzzy-AHP.

For example let us take SITE-2 & SITE-4 it is found that from Table 5.7 that in these sites most of its ‘Actual’ and ‘Passing’ performance values are similar, except for only one indica-tor. But the output from Ideal Position approach gives the same value for both the sites and the difference is the maximum, which in reality is not acceptable. This is the special case for Ideal Position approach because of 2 alternatives situation. Also for Site-1 & Site-3 it is found


& Lamda=0 & Lamda=0.5 & Lamda=1

FOR SITE 1 ACTUAL 0.49556 0.42538 0.46216

PASSING 0.50444 0.57462 0.53784

GRADE Copper Copper Copper

FOR SITE 2 ACTUAL 1 1 1

PASSING 0 0 0

GRADE Gold Gold Gold

FOR SITE 3 ACTUAL 1 1.5208 1.5458

PASSING 1 0.4792 0.45416


FOR SITE 4 ACTUAL 1 1 1

PASSING 0 0 0


Table 5.7: Results of FUZZY-AHP using IDEAL POSITION APPROACH


50

that it has the possibility of RANK REVERSAL when alpha & lambda are 0 and it gives clear results differentiating ‘Actual’ and ‘Passing’ when alpha & lambda are greater than 0. Impor-tantly for Site-3 both the actual & passing grade performances are same when alpha and lambda are 0, and when we increase lambda to 0.1 the performances becomes 1.5201 for Ac-tual & 0.4799 for Passing. This significant jump due to the significant change introduced in the Indicator P1.6 value in the performance level. When alpha & lambda are 0.1, the perform-ance of P1.6 for Actual was 0.8681 and Passing was 0.4964 and when lambda becomes 0 the Actual becomes 0.6247 and Passing becomes 0.7809. This reversal in performance has made the performances equal.

5.4. Evaluation in Fuzzy Reasoning Approach

In Fuzzy reasoning approach, input values can be either verbal or numeric. If it is verbal (lin-guistic) then it can be directly used in the fuzzy inference to get the output linguistic class. If it is numeric then it is fuzzified first. These fuzzified values are integrated using Fuzzy Inference process, which does rule implications and rule aggregation. This process is repeated at differ-ent levels till the final single value at principle level is reached. Triangular Membership curve with Medium slope is used as the main fuzzification in the present study. Table 5.8, 5.9 & 5.10 describes the step by step evaluation of inputs in fuzzy reasoning model.

INPUT INDICATOR P1_3 INDICATOR_P1_1 INDICATOR P1_2 INDICATOR P1_4

0.6032 (Fair) (0.1894) (Poor) 0.7025 (Good) 1 (fair)

AFTER FUZZIFICATION FAIR (0.5872) BAD (0.2424) FAIR (0.19 ) Fair (1) GOOD (0.4128) POOR (0.7576) GOOD (0.81)

FUZZY INFERENCING (Using Min Operator) (Using Max operator)

P1_3 P1_1 P1_2 P1_4 RULE

IMPLICATION RULE AGGREGA-

TION FAIR (0.5872) BAD (0.2424) FAIR (0.19) Fair (1) POOR (0.19) FAIR (0.5872) BAD (0.2424) GOOD (0.81) Fair (1) POOR (0.2424) POOR (0.2424) FAIR (0.5872) POOR (0.7576) FAIR (0.19) Fair (1) FAIR (0.19) FAIR (0.5872) POOR (0.7576) GOOD (0.81) Fair (1) FAIR (0.5872) GOOD (0.4128) BAD (0.2424) FAIR (0.19) Fair (1) POOR (0.19) GOOD (0.4128) BAD (0.2424) GOOD (0.81) Fair (1) POOR (0.2424) FAIR (0.5872) GOOD (0.4128) POOR (0.7576) FAIR (0.19) Fair (1) POOR (0.19) GOOD (0.4128) POOR (0.7576) GOOD (0.81) Fair (1) FAIR (0.4128) CENTROID = 0.422

Table 5.8: Steps involved in “Area_Management” Fuzzy Reasoning Model

(Site-1 Actual Data)


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INPUT INDICATOR P1_5 INDICATOR_P1_6

1(Fair) 1 (Fair) AFTER FUZZIFICATION Fair (1 ) Fair (1 ) FUZZY INFERENCING (Using Min Operator) (Using Max operator)

INDICATOR_P1_5 INDICATOR_P1_6 RULE_IMPLICATION RULE AGGREGATION Fair (1 ) Fair (1 ) Fair (1 ) Fair (1 ) centroid = 0.5

Table 5.9: Steps involved in “Forest_Management” Fuzzy Reasoning Model

(Site-1 Actual Data)

INPUT AREA_MANGEMENT FOREST_MANAGEMENT

0.422 0.5 AFTER FUZZIFICATION AREA_MANGEMENT FOREST_MANAGEMENT

POOR (0.31183) Fair (1) FAIR (0.68817)

FUZZY INFERENCING (Using Min Operator) (Using Max operator)

AREA_MANGEMENT FOREST_MANAGEMENT RULE_IMPLICATION RULE AGGREGATION POOR (0.31183) Fair (1) COPPER(0.31183) COPPER (0.31183)

FAIR (0.68817) Fair (1) BRONZE (0.68817) BRONZE (0.68817) FINAL CENTROID = 0.4134 (DEFUZZIFICATION) The Final Grades are COPPER (0.3464) BRONZE (0.6536)

Table 5.10: Integration of AM & FM outputs in “Forest_Resources_Sustainability” Fuzzy

Reasoning Model (Site-1 Actual Data)


52

Table 5.11 provides the outputs from this approach for different sites. The backbone of this approach is the Expert rules & Membership curves. Sensitivity analysis & Consistency check are carried out to analyse the role of these two major forces. In order to understand the impact of the expert knowledge base over different levels and to check the consistency of the Deci-sion maker we have to analyse all possible values of every parameter (verifier or indicator or criteria) within the model. This is done through simulation. Sub-routines were written in MATLAB to find the output values when different possible input values are provided for every parameter. This parametric analysis has provided the approximate % of contribution of each parameter in impacting the output from its immediate hierarchical level (This is obtained through Multiple Regression analysis, with 77% confidence having deviations less than 0.08). This is repeated for all the levels and we got the relative % of contribution at different levels as depicted in Figure 5.1. Apart from finding out approximate relative % of contribution we should also be sure about the experts consistency about the rules. This is done through Cognitive Mapping Approach.

5.4.1. Cognitive Mapping Process

In this process Experts mental view about the interactions of different ground parameters have to be mapped. So along with Expert rules we have to obtain Cognitive Map also. The cogni-tive map, which is assumed to be obtained from expert for the current research is as depicted in Figure 5.2.

Triangular Gaussian Trapezoidal SITE 1 Actual 0.4134 0.43617 0.4455 Passing 0.5 0.50189 0.5 Grade Copper Copper Copper

SITE 2 Actual 0.3981 0.42564 0.41432 Passing 0.3981 0.42564 0.41432 Grade Bronze Bronze Bronze

SITE 3 Actual 0.75 0.7101 0.75 Passing 0.5 0.50204 0.5 Grade Silver Silver Silver


Table 5.11: Output From the Fuzzy Reasoning Model


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5.4.1.1 Calculation of Direct Force & Central Force From this map we can find out how each verifier is impacting other verifiers in its immediate vicinity & at different neighbourhood. This can be explained by taking an example of ‘Stake Holders Agreement (SHA) Verifier’. From Figure 5.2 it is clear that SHA has 4 immediate impact points (i.e., legal fulfilment, boundary delineation & quality, encroachment, institu-tional & community participation), say ‘First Order Concepts’. So we can say the Direct Force from this verifier is 4. Next we will find role of these first order concepts in affecting others. We will find that these 4 concepts have interactions among themselves and apart from that they have 2 more new concepts (i.e., Increased damage due to forest fire and Missing Early Warning System). So in the 2nd order we have 2 concepts. If we go further, we will come to know that these 2nd order concepts are having interactions with 7 other concepts (i.e., Forest Plan as per land capability, Forest Plan as per Forest Classification, Implementation of Production & Protection forest, Missing Stand structure, Missing Species composition, Miss-ing Skilled Labour, Increased Damage due to other disturbances). Figure 5.3 depicts this in-teraction clearly. From the above we can find out Central Force as per the definition in Chap-ter 4.5.1.

Central Force = 4/1 + 2/2 + 7/3 = 4 + 1 + 2.33 = 7.33 = 7

Central force represents the overall role played by each verifier in the whole process. Similarly we can calculate Direct & Central force for each Verifier. Table 5.13 has the central force ex-erted by all parameters. 5.4.1.2 Identification of Forward & Backward Routes

Using Cognitive Mapping we can also find the different path in which each verifier can par-ticipate in affecting other verifiers. This done through identifying forward and backward routes. Forward route can be called “Consequence” because it affects other in the forward di-rection. Backward route is called “Explanation”, because it is affected by others. By identify-ing participation in number of different routes we can approximately categorize the verifier as a ‘Pressure’ variable if its contribution in forward route is dominant or as a ‘Response’ Vari-able if its contribution in backward route is more. This will help us to model the phenomenon better. It is difficult to differentiate/associate verifiers with ‘Status’ variable due to their dy-namic nature. Table 5.12 describes quantitatively the participation of each verifier in forward & backward routes. By this approach we can identify the “Critical” verifier which participates in many routes, but did not get enough performance on the ground. 5.4.1.3 Consistency Check In order to make sure that the experts view is consistent about the ground process, we have to compare the results of cognitive mapping and parameter analysis. From the parameter analysis we have found out the % of contribution from each verifier and hence we can order the veri-fier within each indicator. From cognitive mapping ‘Central Force’, we can also order the verifiers within each indicator. In principle both should be same, because both are extracted from experts view only. Any deviation in order will tell the inconsistency in that parameter. Table 5.13 clearly depicts the consistency check over experts view. Though most of them


54

matches in the present case, two verifiers (mismatch of protection & Production forest plan as per forest classification map & Encroachment) have order of deviation of magnitude ‘2’, which needs more attention in that 2 verifiers definition either in the RULE BASE or in the COGNITIVE MAP. In-Consistency value = (Deviations encountered / total possible deviation) In the present case, In-consistency value (at verifier level) = 12 / 56 = 0.214 The ‘total possible deviation’ is the sum of possible deviations of individual verifiers. For ex-ample for Indicator P1.1, there are 3 verifiers, so each verifier can deviate maximum by value 3 only, so total deviations for indicator P1.1 is 9. Deviation encountered is the sum of actual deviation found for each verifier. The same can be repeated for different levels. Since in the present research the cognitive map and Rule base are obtained from different groups it is not advised to compare them, but rather the approach shall help the future work in this line.


55

Triangle Gauss Trapezoid

1 Stake Holders Disagreement 76% 75% 76%

INDICATOR_P1.1 2 Problem in Boundary demarcation and implementation 20% 21% 20%

30.5%, 30.4%, 30.3% 3 Missing Legal fulfilment 4% 4% 4%

4 mismatch of protection and production forest plan with land capa-bility map

50% 50% 50%

INDICATOR_P1.2

5 mismatch of protection and production forest plan with Forest Classification

12% 12% 12%

14.4%, 14.8%, 14.7% 6 Problem in implementing protection and production forest plan 38% 38% 38%

AREA MANAGEMENT 7 Increased Damage due to forest fire 31% 31% 31%

83%, 84%, 84% INDICATOR_P1.3 8 encroachment 22% 22% 22%

54.7%, 54.4%, 54.6% 9 forest loss due to Overcutting 24% 24% 24%

10 Increased Damage due to Other disturbances 23% 23% 23%

11 Missing early warning system 52% 51% 52%

INDICATOR_P1.4 12 missing skill labour 34% 35% 34%

0.4%, 0.4%, 0.4% 13 Missing community and institutional participation 14% 14% 14%

FOREST RESOURCES

SUSTAINABILITY 14 Missing silviculture Implementation system 80% 80% 80%

INDICATOR_P1.5 15 missing ecosystem compliance 14% 15% 14%

82%, 82%, 82%

16 Missing Stand structure information, Missing Species composi-tion information, Missing Tree regeneration information

6% 5% 6%

FOREST MANAGEMENT

17%, 16%, 16% INDICATOR_P1.6 17 Non-Availability of Non-Timber Forest Products (NTFP) 58% 57% 58%

18%, 18%, 18% 18 Non-availability of Potential existing number and extraction number of NTFP 42% 43% 42%

Figure 5.1: Relative Percentage of Contribution from Different Parameters at different levels (Using different Membership functions)


56

StakeHolders agreement

Plan as per LC

Plan as per FC

Implementation

Forest Firedamage

Other dist.

overcutting

Early WarningSystem Skill labour

Comm, inst,participation

SilvicultureImplementation

Ecosystemcompliance

Stand structure

Speciescomposition

Tree regeneration

Type of NTFP


Legalfulfillment

Boundary

Encroachment

A B (means A is influenced by B )

A B (means A influences B )

P1.3

P1.2P1.4

P1.5

P1.1

P1.6

StakeHolders agreement

Plan as per LC

Plan as per FC

Implementation

Forest Firedamage

Other dist.

overcutting

Early WarningSystem Skill labour

Comm, inst,participation

SilvicultureImplementation

Ecosystemcompliance

Stand structure

Speciescomposition

Tree regeneration

Type of NTFP


Legalfulfillment

Boundary

Encroachment





P1.3

P1.2P1.4

P1.5

P1.1

P1.6

Figure 5.2: Causal Relationship Diagram of Different Verifiers


57

Stake holders

agreement

Legal fulfillment

encroachment

Boundary problem

Inst. & community particpation

Missing early warning system

forest fire

Missing skill labour

Increased damage due to

other disturbances

Plan as perLand capability

Red – 1st levelBlue – 2nd LevelGreen – 3rd Level

Plan as perForest Classification

Forest Plan Implementation Missing Stand

Structure Information

Missing Species Information

Stake holders

agreement

Legal fulfillment

encroachment

Boundary problem

Inst. & community particpation

Missing early warning system

forest fire

Missing skill labour

Increased damage due to

other disturbances

Plan as perLand capability

Red – 1st levelBlue – 2nd LevelGreen – 3rd Level

Plan as perForest Classification

Forest Plan Implementation Missing Stand

Structure Information

Missing Species Information

Figure 5.3: Direct & Central Forces Exerted By ‘Stake Holders Agreement’ Verifier


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Table 5.12: Role of Verifiers in the Forward & Backward Routes

List of all concepts. Forward Routes Backward Routes VARIABLE TYPE

(Consequences) (Explanation) DEDUCED

(Branch, Heads) (Branch, Tails)

Stake Holders Disagreement 4,43 0,0 PRESSURE

Problem in Boundary demarcation and implementation 1,1 2,2 RESPONSE

Missing Legal fulfilment 2,2 1,1 PRESSURE

Mismatch of protection and production forest plan with land cover map 2,7 1,2 PRESSURE

Mismatch of protection and production forest plan with Forest Classification 4,6 2,8 BOTH

Problem in implementation of protection and production forest plan 0,0 3,16 RESPONSE

Increased Damage due to forest fire 5,18 3,4 PRESSURE

Encroachment 0,0 5,7 RESPONSE

Increased Damage due to Other disturbances 0 3,27 RESPONSE

Missing early warning system 3,20 2,2 PRESSURE

Missing skill labour 3,39 0 PRESSURE

Missing community and institutional participation 3,39 1,1 PRESSURE

Missing silviculture Implementation system 0,0 4,33 RESPONSE

Missing ecosystem compliance 1,1 1,8 RESPONSE

Missing Stand structure information 1,1 2,12 RESPONSE

Missing Species composition information 3,3 2,12 RESPONSE

Missing Tree regeneration information 1,1 0 PRESSURE

Non-Availability of Non-Timber Forest Products (NTFP) 1,1 1,12 RESPONSE

Non-availability of Potential existing number and extraction number of NTFP 1,1 2,24 RESPONSE

Consequences - It impacts others Branch - gives the immediate one step ahead in the forward route

Heads - gives all possible forward routes till end

Explanation - This is caused by others Branch - gives the one step behind in the backward route

Tails - gives all possible backward routes till end


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ORDER ORDER Order List of all concepts. PARAMETER ANALYSIS OF COGNITIVE MAPPING OF Deviation

(% of Contribution) IMPORTANCE (Central Force) IMPORTANCE 1 Stake Holders Disagreement 76% 1 7 1 0 2 Problem in Boundary demarcation and implementation 20% 2 5 2 0 3 Missing Legal fulfilment 4% 3 5 2 1 4 mismatch of protection and production forest plan with land capability map 50% 1 8 2 1 5 mismatch of protection and production forest plan with Forest Classification 12% 3 10 1 2 6 Problem in implementation of protection and produc-tion forest plan 38% 2 8 2 0 7 Increased Damage due to forest fire 31% 1 12 1 0 8 encroachment 22% 4 8 2 2 9 forest loss due to Overcutting 24% 2 10 Increased Damage due to Other disturbances 23% 3 7 3 0 11 Missing early warning system 52% 1 10 1 0 12 missing skill labour 34% 2 9 2 0 13 Missing community and institutional participation 14% 3 9 2 1 14 Missing silviculture Implementation system 80% 1 8 2 1 15 missing ecosystem compliance 14% 2 6 3 1 16 Missing Stand structure information, 6% 3 8 2 1 Missing Species composition information 9 1 Missing Tree regeneration information 3 4 17 Non-Availability of Non-Timber Forest Products (NTFP) 58% 1 6 2 1 18 Non-availability of Potential existing number and ex-traction number of NTFP 42% 2 7 1 1

Table 5.13: Consistency Check between Experts Rules and His Views on Ground Interaction


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5.4.2. Sensitivity Analysis

5.4.2.1 Using Different Confidence levels for Membership Curve In the fuzzy reasoning model, two major parameters are considered to be its major strength and also its weakness. First one is the membership curve and second one is the Expert Rules. In order to check the role of membership curve in the fuzzy model, I have considered 3 different types of membership curve: Triangular, Gaussian and Trapezoidal. These Membership func-tions are considered as representation of different confidence levels of the decision maker, shown in Figure 5.4. Triangular membership curve represents that the decision maker is least confident because he is very uncertain about belongingness of any value to a particular linguis-tic class except at one point for each. Trapezoidal curve represents that decision maker the most confident, because he is very certain about the belonging of certain range of values to particular class and Gaussian curve represent the moderate confidence level. The fuzzy reasoning model is analysed for all the 4 sites using 3 different membership func-tions. The output from the model is shown in the Table 5.11. It is found that the absolute quan-titative performances of the outputs from ‘Actual’ & ‘Passing’ Grade vary with the shape and the performance is maximum for Trapezoidal membership (most confident) in most of the cases. Gaussian shape produces next higher performance in output and finally triangular mem-bership having lowest in many cases (least confident). From this it can be said that when the uncertainty associated with the membership is higher then the output performance is lower and vice versa. 5.4.2.2 Using Different Attitudes for Membership Curve Apart from having different Confidence (as Shape), the membership curves are also tested for different Attitude (as slope). Three kind of attitude like Strict, Moderate and Liberal are consid-ered by having membership curves with different slopes (Fig. 5.5). When the decision maker is of Strict nature, he will try to have narrow range of input values as members of particular class. This is considered by having steep slope. If he is Liberal Attitude person then he will try to have more range of input values as a members of a particular class and this is implemented as gentle slope curve. The Moderate Attitude is finally represented as having moderate slope (in between Steep and Gentle). Table 5.14 shows the output from these different slopes.


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Least Confidence

'Bad':[0.00 0.00 0.25]

'Poor':[0.00 0.25 0.50]

'Fair':[0.25 0.50 0.75]

'Good':[0.50 0.75 1.00]

‘Excellent':[0.75 1.00 1.00]

Moderate Confidence

'Bad’:[0.1062 0.00]

'Poor':[0.1062 0.25]

'Fair':[0.1062 0.50]

‘Good':[0.1062 0.75]

'Excellent':[0.1062 1.00]

Most Confidence

'Bad':[0.000 0.000 0.025 0.225]

'Poor':[0.025 0.225 0.275 0.475]

'Fair':[0.275 0.475 0.525 0.725]

'Good':[0.525 0.725 0.775 0.975]

'Excellent':[0.7724 0.9724 1.00 1.00]

Least Confidence

'Bad':[0.00 0.00 0.25]

'Poor':[0.00 0.25 0.50]

'Fair':[0.25 0.50 0.75]

'Good':[0.50 0.75 1.00]

‘Excellent':[0.75 1.00 1.00]

Least Confidence

'Bad':[0.00 0.00 0.25]

'Poor':[0.00 0.25 0.50]

'Fair':[0.25 0.50 0.75]

'Good':[0.50 0.75 1.00]

‘Excellent':[0.75 1.00 1.00]

Moderate Confidence

'Bad’:[0.1062 0.00]

'Poor':[0.1062 0.25]

'Fair':[0.1062 0.50]

‘Good':[0.1062 0.75]

'Excellent':[0.1062 1.00]

Moderate Confidence

'Bad’:[0.1062 0.00]

'Poor':[0.1062 0.25]

'Fair':[0.1062 0.50]

‘Good':[0.1062 0.75]

'Excellent':[0.1062 1.00]

Most Confidence

'Bad':[0.000 0.000 0.025 0.225]

'Poor':[0.025 0.225 0.275 0.475]

'Fair':[0.275 0.475 0.525 0.725]

'Good':[0.525 0.725 0.775 0.975]

'Excellent':[0.7724 0.9724 1.00 1.00]

Most Confidence

'Bad':[0.000 0.000 0.025 0.225]

'Poor':[0.025 0.225 0.275 0.475]

'Fair':[0.275 0.475 0.525 0.725]

'Good':[0.525 0.725 0.775 0.975]

'Excellent':[0.7724 0.9724 1.00 1.00]

Figure 5.4: Membership Curves with Different Confidence Levels


62

'Bad':[0.00 0.00 0.20]

‘Poor':[0.05 0.25 0.45]

'Fair':[0.30 0.50 0.7]

'Good':[0.55 0.75 0.95]

'Excellent':[0.80 1.00 1.00]

Strict Attitude

'Bad':[0.00 0.00 0.30]

‘Poor':[-0.05 0.25 0.55]

'Fair':[0.20 0.50 0.80]

'Good':[0.45 0.75 1.00]

'Excellent':[0.70 1.00 1.00]

Liberal Attitude

'Bad':[0.00 0.00 0.25]

'Poor':[0.00 0.25 0.50]

'Fair':[0.25 0.50 0.75]

'Good':[0.50 0.75 1.00]

‘Excellent':[0.75 1.00 1.00]

Moderate Attitude

'Bad':[0.00 0.00 0.20]

‘Poor':[0.05 0.25 0.45]

'Fair':[0.30 0.50 0.7]

'Good':[0.55 0.75 0.95]

'Excellent':[0.80 1.00 1.00]

Strict Attitude

'Bad':[0.00 0.00 0.20]

‘Poor':[0.05 0.25 0.45]

'Fair':[0.30 0.50 0.7]

'Good':[0.55 0.75 0.95]

'Excellent':[0.80 1.00 1.00]

Strict Attitude

'Bad':[0.00 0.00 0.30]

‘Poor':[-0.05 0.25 0.55]

'Fair':[0.20 0.50 0.80]

'Good':[0.45 0.75 1.00]

'Excellent':[0.70 1.00 1.00]

Liberal Attitude

'Bad':[0.00 0.00 0.30]

‘Poor':[-0.05 0.25 0.55]

'Fair':[0.20 0.50 0.80]

'Good':[0.45 0.75 1.00]

'Excellent':[0.70 1.00 1.00]

Liberal Attitude

'Bad':[0.00 0.00 0.25]

'Poor':[0.00 0.25 0.50]

'Fair':[0.25 0.50 0.75]

'Good':[0.50 0.75 1.00]

‘Excellent':[0.75 1.00 1.00]

Moderate Attitude

'Bad':[0.00 0.00 0.25]

'Poor':[0.00 0.25 0.50]

'Fair':[0.25 0.50 0.75]

'Good':[0.50 0.75 1.00]

‘Excellent':[0.75 1.00 1.00]

Moderate Attitude

Figure 5.5: Membership Curves with Different Attitudes


63

From Table 5.14 it is found that when slope increases (attitude changes from Liberal to Strict) the outputs of ‘Actual’ & Passing grade becomes equal in most of the cases. This can be due to the fact that when slope increases the fuzziness (overlap area) between two adjacent member-ship curves decreases and hence the model is not able to differentiate small variations in the inputs (because we have considered Max-Min composition, Minimum value will be taken). On the other hand when the slope decreases, overlap between two adjacent membership curves (of linguistic classes) increases and hence the smaller difference in the input is differentiated well and finally this leads to the bigger difference in the outputs. But at the same time, if the slope decreases beyond certain value then it will lead to the overlap with the third membership curve and hence diluting overall membership strength. This will mislead the fuzzy inference to differ-entiate the significance in the output strength. In our case outputs using Medium slope member-ship curves has the bigger difference in ‘Actual’ & ‘Passing’ performance values, this is due to the fact that this membership has the highest possible overlap between two adjacent member-ship curves. Membership curves with Minimum slope have overlap with 3 adjacent member-ships and hence it has produced less difference in most of the cases. Here we can also say that when the decision maker is more liberal (gentle slope) he is more un-certain. So from the results we can say that if the uncertainty increases the output performances decreases and here care must be taken not to consider too strict attitude (though this is assumed to be more certain).

Strict Attitude Moderate Attitude Liberal Attitude SITE 1 Actual 0.5 0.4134 0.38906 Passing 0.5 0.5 0.5

Grade Bronze Copper Copper

SITE 2 Actual 0.46044 0.3981 0.38359 Passing 0.46044 0.3981 0.38359

Grade Bronze Bronze Bronze

SITE 3 Actual 0.75 0.75 0.6614 Passing 0.5 0.5 0.5

Grade Silver Silver Bronze


Table 5.14: Fuzzy Model output from membership curve with different attitudes


64

5.4.2.3 Variation of output while varying Input values To find out how sensitive the model is to the small variation in the input, we have to add or subtract small fraction of values and check the output variation. MATLAB functions were writ-ten to do this sensitivity analysis. The variation in output is studied by adding small fraction of values to the input variables that belongs Area Management, because the relative contribution from Area Management is more than 80% for the final performance. For this analysis I have considered the Site-1 Data. From the parameter analysis it is clear that relative contribution from P1.3 plays the first important role and P1.1 is playing next important role in achieving Area Management performance. So I have checked the variation of these parameters with respect to some fractions. Table 5.15 a & b shows the outcome of this analysis over Indicator P1.3 and Indicator P1.1 respectively. The possible input range of any input parameter is considered between 0 to 1 in the fuzzy model. It is a general interesting belief that “if a parameter/criteria/indicator is important then the small variations of that parameter/criteria/indicator should contribute significantly to the output per-formance”. But there is a pit fall in this assumption, because in the Sustainability issue, if a pa-rameter is important and if that parameter is made very sensitive in the model then higher per-formance of that parameter will take the output of evaluation to a higher level. In such case, on the ground the management team will put full effort in making only that parameter to a higher performance level so that bad performances of other parameters/criteria/indicator are automati-cally overlooked. So a good model should not be too sensitive to the most important criteria and in the case of saturated performance of those criteria the model should also consider other important parameters. At this juncture most of the existing MCDM methods fail to fulfil this need. But Fuzzy Reasoning Model Wonderfully considers this vital role and it is visible in the following sensitivity discussion. Fraction Changed

Area Manage-ment Output

Forest Management Output

Forest Resources Sus-tainability Output

Change in output w.r.t. Actual output

P1.3 + 0.001 0.4218 0.92 0.4132 -0.0002 P1.3 + 0.01 0.4194 0.92 0.4116 -0.0018 P1.3 + 0.1 0.4294 0.92 0.4187 0.0053 P1.3 + 0.2 0.4294 0.92 0.4187 0.0053 P1.3 + 0.3 0.4241 0.92 0.4148 0.0014 P1.3 – 0.3 0.3142 0.92 0.326 -0.0874 P1.3 – 0.2 0.3978 0.92 0.3941 -0.0193 P1.3 – 0.1 0.4294 0.92 0.4187 0.0053 P1.3 – 0.01 0.4243 0.92 0.415 0.0016 P1.3-0.001 0.4223 0.92 0.4136 0.0002 Table 5.15a: Sensitivity of the Model with respect to input variations in Indicator P1.3


65

Fraction Changed

Area Manage-ment Output

Forest Management Output

Forest Resources Sus-tainability Output

Change in output w.r.t. Actual output

P1.1 + 0.001 0.4229 0.92 0.414 0.0006 P1.1 + 0.01 0.4314 0.92 0.4203 0.0069 P1.1 + 0.1 0.4909 0.92 0.4856 0.0722 P1.1 – 0.1 0.4294 0.92 0.4187 -0.0575 P1.1 – 0.01 0.4243 0.92 0.415 -0.0063 P1.1-0.001 0.4223 0.92 0.4136 -0.0006

Table 5.15b: Sensitivity of the Model with respect to input variations in Indicator P1.1 In Table 5.15a it is seen that when most important parameter P1.3 is added fractions like 0.1 or 0.2 or 0.3, the variation in output is changing only in 3rd and 4th decimal places. Normal user shall wonder that adding 0.3 would take original value (0.6032) of P1.3 to 0.9032, which is close to the maximum performance of that indicator. In this case in the fuzzy model, the output variation was only 0.0014. This is due to the fact that P1.3 is getting saturated and model deals it rationally, by keeping its values under control. So immediately user can assume that if in-creasing makes the saturation, so decreasing should contribute significantly to the output. So fractions were subtracted to see that effect. The results were fabulous, because the important parameter value is reduced it has affected again rationally towards lower output performance. Addition of 0.3 has produced less change in output than the subtraction of 0.3. Hence the role of important parameter is considered in a balanced way. In Table 5.15b it is visible that the maximum fraction considered is 0.1, this is due to fact that the original value of P1.1 is 0.1894, hence 0.1 can be subtracted completely and hence the same is considered for addition also for comparison purposes. In this case, the model has behaved almost in the same manner for addition and subtraction, making the management team to put effort compulsorily towards positive side. When the model is checked for Indicator P1.4, the output is not at all changed for whatever value of P1.4. So we can say that either the indicator P1.4 is redundant or our expert rule/decision tree has not really considered it well. If the later case is true then decision tree has to be revised to include the meaningful role of Indicator P1.4 in the interaction process.

5.5. Type-2 Fuzzy Logic Approach

Type-2 Fuzzy logic approach is similar to normal fuzzy logic (Type-1) approach, except the fact that the membership curves have been modified to include uncertainty components. Two different possible uncertainties associated with triangular membership curve: a) Uncertainty in the base of membership and b) uncertainty in base as well as uncertainty in the highest mem-bership range are examined in the present research. The Type2 membership functions used in the present research are shown in the Figure 5.6 & Figure 5.7


66

Once the possible uncertain range of membership curves are chosen, we can attach Decision Maker’s (DM) Confidence as a weights to each membership curve and these weights can be considered as 3rd dimension. For example, there are 3 Membership curves associated with the Linguistic Class ‘BAD’ (BadU, Bad, BadL). Out of these 3 curves DM is confident about the middle one and can assign the weight of 0.9 and Upper curve (BadU) can get 0.8 or any other and lower one may get 0.7 or any other value. In the present research both the upper and lower membership curves are given weightage of 0.8 and the middle one weightage as 0.9. In the Next step we will be fuzzifying the inputs. Now the every fuzzified value will be attached with the uncertainty weights also. If we consider different weights for upper and lower membership curves then there will be huge number of possible fuzzification values for a single x value hav-ing varying secondary grades, hence for the demonstration purpose only end points are consid-ered for calculation. Table 5.16 shows the type-2 fuzzified values for the inputs from Site-1 data.


67

'BadL':[0.00 0.00 0.20] 'Bad':[0.00 0.00 0.25] 'BadU':[0.00 0.00 0.30]

'PoorL':,[0.10 0.25 0.40] 'Poor':[0.05 0.25 0.45] ‘PoorU':[0.00 0.25 0.50]

'FairL':[0.30 0.50 0.70] 'Fair':[0.25 0.50 0.75] 'FairU':[0.20 0.50 0.80]

'GoodL':,[0.60 0.75 0.90] 'Good':[0.55 0.75 0.95] 'GoodU':[0.50 0.75 1.00]

'ExcellentL':[0.80 1.00 1.00] 'Excellent':[0.75 1.00 1.00] 'ExcellentU':[0.70 1.00 1.00]

'L’ Stands for Lower End ‘U’ Stands for Upper End

'BadL':[0.00 0.00 0.20] 'Bad':[0.00 0.00 0.25] 'BadU':[0.00 0.00 0.30]

'PoorL':,[0.10 0.25 0.40] 'Poor':[0.05 0.25 0.45] ‘PoorU':[0.00 0.25 0.50]

'FairL':[0.30 0.50 0.70] 'Fair':[0.25 0.50 0.75] 'FairU':[0.20 0.50 0.80]

'GoodL':,[0.60 0.75 0.90] 'Good':[0.55 0.75 0.95] 'GoodU':[0.50 0.75 1.00]

'ExcellentL':[0.80 1.00 1.00] 'Excellent':[0.75 1.00 1.00] 'ExcellentU':[0.70 1.00 1.00]


Figure 5.6: Type-2 Fuzzy Membership Functions & its ranges

(Uncertainty in the Base x-range Values)


68

'BadL':[0.00 0.00 0.20] 'Bad':[0.00 0.00 0.025 0.250] 'BadU':[0.0 0.0 0.04695 0.300]

'PoorL':,[0.10 0.25 0.40] 'Poor':[0.05 0.2276 0.2776 0.45] ‘PoorU':[0.0 0.201 0.2981 0.500]

'FairL':[0.30 0.50 0.70] 'Fair':[0.25 0.475 0.525 0.750] 'FairU':[0.20 0.453 0.5467 0.780]

'GoodL':,[0.60 0.75 0.90] 'Good':[0.55 0.725 0.775 0.950] 'GoodU':[0.5 0.7100 0.794 1.000]

'ExcellentL':[0.80 1.00 1.00] 'Excellent':[0.75 0.975 1.000 1.000] 'ExcellentU':[0.7 0.9561 1.000 1.000]


'BadL':[0.00 0.00 0.20] 'Bad':[0.00 0.00 0.025 0.250] 'BadU':[0.0 0.0 0.04695 0.300]

'PoorL':,[0.10 0.25 0.40] 'Poor':[0.05 0.2276 0.2776 0.45] ‘PoorU':[0.0 0.201 0.2981 0.500]

'FairL':[0.30 0.50 0.70] 'Fair':[0.25 0.475 0.525 0.750] 'FairU':[0.20 0.453 0.5467 0.780]

'GoodL':,[0.60 0.75 0.90] 'Good':[0.55 0.725 0.775 0.950] 'GoodU':[0.5 0.7100 0.794 1.000]

'ExcellentL':[0.80 1.00 1.00] 'Excellent':[0.75 0.975 1.000 1.000] 'ExcellentU':[0.7 0.9561 1.000 1.000]


Figure 5.7: Type-2 Fuzzy Membership Functions & its ranges

(Uncertainty in the Base x-range Values & Uncertainty in Highest Membership Value range)


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These fuzzified values are then fed to fuzzy inference engine to produce the output. This fuzzy inferencing mechanism is similar to type-1 fuzzy approach, but the way the strength of mem-bership calculated is different in type-2 approach. The Possible Rule combination and type-2 rule strength evaluation (rule1) for AM, FM & FRS part of site-1 is given detailed in the Table 5.17 (a,b) , 5.18, 5.19 & Table 5.20.

0.8 0.9 0.8 p11_poor= 0.8 0.9 0.8 p11_bad=

0.053 0.2424 0.3687 0.596 0.697 0.758

0.8 0.9 p12_good= 0.8 0.9 0.8 p12_fair=

0.325 0.19 0.6833 0.7625 0.81 p13_fair= 0.8 0.9 0.8 p13_good= 0.8 0.9 0.8

0.484 0.5872 0.656 0.0213 0.266 0.413

p14_fair= 0.9 p15_fair= 0.9 1 1 p12_excel= 0.8 p16_fair= 0.9 0.0083 1

Table5.16: Type-2 Fuzzified values of Inputs from Site-1

Possible Rule Com-

bination INDICA-

TOR_P1_3 INDICA-

TOR_P1_1 INDICA-

TOR_P1_2 INDICA-

TOR_P1_4 RULE_IMPLICATION RULE AGGRE-

GATION

Rule 1 FAIR BAD FAIR FAIR POOR Rule 2 GOOD BAD FAIR FAIR POOR POOR Rule 3 FAIR POOR FAIR FAIR FAIR Rule 4 GOOD POOR FAIR FAIR POOR Rule 5 FAIR BAD GOOD FAIR POOR Rule 6 GOOD BAD GOOD FAIR POOR Rule 7 FAIR POOR GOOD FAIR FAIR Rule 8 GOOD POOR GOOD FAIR FAIR FAIR Rule 9 FAIR BAD EXCELLENT FAIR POOR Rule 10 GOOD BAD EXCELLENT FAIR POOR Rule 11 FAIR POOR EXCELLENT FAIR FAIR Rule 12 GOOD POOR EXCELLENT FAIR FAIR

Table 5.17a: Possible Rules applied to Site-1 data over AM


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After fuzzification, the inputs P11 gets membership in 2 linguistic classes, P12 has 3 linguistic classes, P13 has 2 and P14 has 1 linguistic class respectively. When these are fed to AM infer-encing, they make combination (2*3*2*1=12). These 12 combinations are evaluated as 12 rules from the knowledge base. Then we have to find out the strength of these rules outcome. In the normal type-1 fuzzy approach strength of the rule is calculated using SUP * composition, which usually takes MAX (MIN) approach, means rule implication takes AND operation (Minimum) and rule aggregation takes the OR operation (maximum value). Moreover in nor-mal type-1 fuzzy approach a single input will have only one possible membership value in one linguistic class, but in the present study type-2 approach will take 3 membership values for a single linguistic class (e.g., one for BadU, another for Bad and final one for BadL) hence the Rule evaluation using MAX (MIN) composition is not straight forward. We have to use the definition proved by Mendel (2000) as explained in the Appendix F. This is explained in a step-by-step manner for the RULE1 of AM inferencing (Table 5.19) the values are taken from Table 5.16. Similarly we can deduce the rule strength for all needed rules. Since FM has only one rule and all belongs to single class with single membership value it gets directly the strength as specified in Table 5.17b. Once AM & FM outputs are ready we can do fuzzy inferencing for FRS. From AM we are get-ting 2 outputs (Poor and Fair) and from FM we are getting 1 output (Fair) and hence they make together 2 possible combinations as mentioned in Table 5.18. Rule strength evaluation for FRS outputs is also shown in Table 5.20

AREA_MANGEMENT FOREST_MANAGEMENT RULE_IMPLICATION RULE AGGREGA-

TION POOR FAIR COPPER COPPER

FAIR FAIR BRONZE BRONZE

Table 5.18: Possible Rule combination at FRS level (SITE-1)

INDICATOR_P1_5 INDICATOR_P1_6 RULE_IMPLICATION RULE AGGREGA-

TION Fair (0.9/1) Fair (0.9/1) Fair (0.9/1) Fair (0.9/1)

Table 5.17b: Fuzzy Inferencing applied to Site-1 data over AM


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0.8 ^0.8 0.8 ^0.9 0.8 ^0.8 0.9 ^0.8 0.9 ^0.9 0.9 ^0.8 0.8 ^0.8 0.8 ^0.9 0.8 ^0.8

P13_Fair AND P11_Bad = 0.484 ^ 0.0530 0.484 ^ 0.2424 0.484 ^ 0.3687 0.5872 ^ 0.0530 0.5872 ^ 0.2424 0.5872 ^ 0.3687 0.6560 ^ 0.0530 0.6560 ^ 0.2424 0.6560 ^ 0.3687

0.8 0.8 0.8 0.8 0.9 0.8 0.8 0.8 0.8 P13_Fair AND P11_Bad =

0.053 0.2424 0.3687 0.053 0.2424 0.3687 0.053 0.053 0.2424

max(0.8,0.8,0.8) max(0.8,0.9,0.9) max(0.8,0.8,0.8) Where ^ refers to AND operation (minimum function) P13_Fair AND P11_Bad =

0.053 0.2424 0.3687

0.8 0.9 0.8 P13_Fair AND P11_Bad =

0.053 0.2424 0.3687

0.8^0.9 0.9^0.9 P12_Fair AND P14_Fair =

0.325^1 0.19^1

0.8 0.9 P12_Fair AND P14_Fair =

0.325 0.19

0.8 ^ 0.8 0.8 ^ 0.9 0.9 ^ 0.8 0.9 ^ 0.9 0.8 ^ 0.8 0.8 ^ 0.9 P13_FAIR and P11_Bad AND P12_Fair AND P14_Fair =

0.0530 ^ 0.325 0.0530 ^ 0.19 0.2424 ^ 0.325 0.2424 ^ 0.19 0.3687 ^ 0.325 0.3687 ^ 0.19

0.8 0.8 0.8 0.9 0.8 0.8 P13_FAIR and P11_Bad AND P12_Fair AND P14_Fair =

0.053 0.053 0.2424 0.19 0.325 0.19

MAX(0.8,0.8) MAX(0.8,0.9) 0.8 0.8 P13_FAIR and P11_Bad AND P12_Fair AND P14_Fair =

0.053 0.19 0.2424 0.325

0.8 0.9 0.8 0.8 P13_FAIR and P11_Bad AND P12_Fair AND P14_Fair =

0.053 0.19 0.2424 0.325

Table 5.19: Type-2 Rule Strength Evaluation for Rule-1 in Area Management Part of Site-1


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0.8 0.8 0.8 0.8 0.8 AM_OUTPUT_POOR =

0.19 0.2424 0.266 0.325 0.3687

0.8 0.8 0.8 0.8 AM_OUTPUT_POOR =

0.484 0.5872 0.596 0.656

0.9 FM_OUTPUT_FAIR =

1

0.8^0.9 0.8^0.9 0.8^0.9 0.8^0.9 0.8^0.9 FRS_OUTPUT_COPPER

0.19^1 0.2424^1 0.266^1 0.325^1 0.3687^1

0.8 0.8 0.8 0.8 0.8

FRS_OUTPUT_COPPER = 0.19 0.2424 0.266 0.325 0.3687

0.8^0.9 0.8^0.9 0.8^0.9 0.8^0.9 FRS_OUTPUT_BRONZE =

0.484^1 0.5872^1 0.596^1 0.656^1

0.8 0.8 0.8 0.8 FRS_OUTPUT_BRONZE =

0.484 0.587 0.596 0.656 Centroid Statistics

MIN MAX MEAN STD Number of Centroids 0.3691 0.4766 0.4327 0.0232 180

Table 5.20: FRS evaluation & Centroid Statistics obtained from

Type-2 Fuzzy Approach (SITE-1)


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Now we have got 2 possible output linguistic classes from FRS level. We have to defuzzify this in order to find out crisp centroid value. In the conventional fuzzy approach it is very sim-ple that each output linguistic classes will have single associated strength and hence it would be simpler to find out the centroid of them. But in the case of Type-2 approach instead of sin-gle value we have different possible primary membership value with different confidence (un-certainty weight) values. In the present SITE-1 analysis we have 5 values for Copper and 4 values for Bronze so there are 20 possible combinations and hence 20 output centroids are pos-sible, provided there is only one membership curve attached to each of the linguistic class. But type-2 approach makes this more complex by having more membership curves attached with every linguistic class. In our case we have 3 linguistic curves for ‘Copper’ & ‘Bronze’ class each, hence total 9 possible combinations among them. Each combination can take 20 values, so finally 9*20=180 centroids can be derived from the present approach. Hence From this ap-proach we can find out how the uncertainties lead to different possible centroids and their dis-tribution.

The type-2 fuzzy logic evaluated outputs (using uncertainty in base) for different sites are tabu-lated in Table 5.21.

It is found from Table 5.21 that Type-2 approach is able to differentiate Site-2 (though the dif-ference is less), which by type-1 approach could not. Also From the standard deviation we can identify the spread of centroid.

PERFORMANCE

MIN MAX MEAN STD Number of Centroids

SITE 1 ACTUAL 0.3691 0.4766 0.4327 0.0232 180 PASSING 0.4995 0.5 0.4998 0.000042 15 GRADE Copper SITE 2 ACTUAL 0.3765 0.4761 0.4362 0.0226 180 PASSING 0.3765 0.4761 0.4338 0.023 324 GRADE Bronze SITE 3 ACTUAL 0.4996 0.5 0.4997 0.000063 9 PASSING 0.2496 0.25 0.2497 0.000065 9 GRADE Silver SITE 4 ACTUAL 0.37 0.4953 0.4528 0.0263 585 PASSING 0.37 0.4872 0.4486 0.0226 585 GRADE Bronze

Table5.21: Outputs from Type-2 Fuzzy Logic using Membership curves having Uncertainty in the Base (X-Range) Only


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The outputs from same type-2 approach but using different uncertainty membership (uncer-tainty in base as well as in highest membership value) have also been calculated for analysing the sensitivity of the model. The results are depicted in Table 5.22 It is found from Table 5.21 & 5.22 that the standard deviation of results from second category of uncertainty is more than the first category it shows that when we add more uncertainty the model is able to represent that effect in the output efficiently. We can say that More the spread of the centroid, more the uncertainty associated. Also one can see that number of centroids in-volved in the second category of membership is more than the first category of memberships, which is also another indication of more possible uncertain areas. Also the difference between ‘Actual’ & ‘Passing’ performance are enhanced in the second category of uncertainty.

PERFORMANCE

MIN MAX MEAN STD Number of Centroids

SITE 1 ACTUAL 0.2753 0.4501 0.3561 0.0447 270 PASSING 0.409 0.5 0.4522 0.0056 21 GRADE Copper SITE 2 ACTUAL 0.2806 0.4454 0.3596 0.0437 315 PASSING 0.2806 0.4454 0.3568 0.0437 486 GRADE Bronze SITE 3 ACTUAL 0.4239 0.5 0.4635 0.005 12 PASSING 0.1817 0.2499 0.2171 0.0042 9 GRADE Silver SITE 4 ACTUAL 0.2679 0.4879 0.3717 0.0516 702 PASSING 0.2679 0.4684 0.3613 0.0477 702 GRADE Bronze

Table 5.22: Outputs from Type-2 Fuzzy Logic using Membership curves having Uncertainty in the Base (X-Range) &

Uncertainty in Highest Membership value


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Area Management Forest Management P.13 P1.1 P1.2 P1.4 P1.5 P1.6 SITE 1 ACTUAL 0.6032 (F) 0.1894 (P) 0.7025 (G) 1 (F) 1 (F) 1 (F) PASSING 0.6032 (F) 0.5 (F) 0.3321 (F) 1 (P) 1 (F) 1 (F) SITE 2 ACTUAL 0.4421 (F) 0.2804 (F) 0.4092 (F) 1 (G) 0.3057 (F) 0.4552 (F) PASSING 0.4421 (F) 0.2804 (F) 0.4092 (F) 0.5868 (F) 0.3057 (F) 0.4552 (F) SITE 3 ACTUAL 1 (F) 0.5724 (F) 0.5 (P) 1 (B) 0.5396 (P) 1 (F) PASSING 0.5 (P) 0.5724 (F) 0.5 (F) 1 (P) 1 (F) 0.5 (P) SITE 4 ACTUAL 0.4425 (F) 1 (E) 0.6408 (F) 0.4516 (F) 0.3835 (F) 0.3719 (F) PASSING 0.4425 (F) 0.2695 (F) 0.6408 (F) 0.4516 (F) 0.3835 (F) 0.3719 (F)

Table 5.23: Input data arranged in importance order

FUZZY-REASONING SHAPE SLOPE

AHP Modified FUZZY-AHP (Pessimistic, Moderate, Optimistic) Triangle Gauss Trapez Steep Moderate Less

TYPE-2 FUZZY REA-SONING

SITE 1 ACTUAL 0.6028 0.50285 0.49438 0.49689 0.4134 0.43617 0.4455 0.5 0.4134 0.38906 0.3691,0.4327,0.4766

PASSING 0.6875 0.49715 0.50562 0.50311 0.5 0.50189 0.5 0.5 0.5 0.5 0.4995, 0.4998, 0.5

SITE 2 ACTUAL 0.4236 0.51475 0.5136 0.51485 0.3981 0.42564 0.41432 0.46044 0.3981 0.38359 0.3765, 0.4362, 0.4761

PASSING 0.3787 0.48525 0.4864 0.48515 0.3981 0.42564 0.41432 0.46044 0.3981 0.38359 0.3765, 0.4338, 0.4761

SITE 3 ACTUAL 0.7359 0.52326 0.52569 0.52703 0.75 0.7101 0.75 0.75 0.75 0.6614 0.4996, 0.4997, 0.5

PASSING 0.7461 0.47674 0.47431 0.47297 0.5 0.50204 0.5 0.5 0.5 0.5 0.2496, 0.2497, 0.25

SITE 4 ACTUAL 0.5961 0.53379 0.52706 0.53034 0.4112 0.44685 0.45243 0.5 0.4112 0.38661 0.37, 0.4528, 0.4953

PASSING 0.3254 0.46621 0.47294 0.46966 0.4041 0.43843 0.43967 0.5 0.4041 0.3841 0.37, 0.4486, 0.4872

Table 5.24: Results from different approach


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5.6. Overall Comparision

In order to make the comparisons of the results from different approach it is better to have a look on input data considered again in a more detailed perception. The input indicators are arranged as per their important order as seen by expert and also have been considered by fuzzy reasoning model. Table 5.23 shows the example input given by experts (important indicators are shown in dark green shade, least important one as lighter yellow shade and orange shade showing the indicators values having performance difference in each site). If only one value has orange shade in a site then for that site that is the only Indicator which has different per-formance and other all are having same performance. Table 5.24 shows the results from vari-ous approaches. 2-tuple approach is not considered for comparison due to its limitations.

Let us consider Site-1 first. According to AHP, the site has failed to get the minimum passing performance and the absolute difference in performance is (0.6875-0.6028) 0.0847 and hence will get Copper Grade. It is visible from the input that only Indicator P1.1 of passing perform-ance & P1.2 of Actual performance is going to make the difference in final performance. From Appendix-B (Table B.3) it is found that the weightage of P1.1 (0.5681) is more than the weightage of P1.2 (0.1333) and hence AHP leads passing performance to higher value. In Modified Fuzzy-AHP the performance difference is very little (0.01124) and hence the deci-sion based on this small difference would be fatal. Also the results are showing rank reversal possibility if the lower scores (pessimistic scenario) are considered. Though the performance from fuzzy reasoning model using triangular membership curve with moderate slope is of lower value but the difference in performance is 0.0866 similar to AHP results, which is due to similar importance preference given for the indicators in the model. For gaussian and trapezoi-dal curves, output performance decreases the difference. Membership curve with steep slope could not differentiate the inputs and hence this type of membership is not to be used. Type-2 fuzzy model results into two non-overlapping triangle and hence we are sure about the failing of actual performance.

Site-2 data represents one extreme input condition, showing that all the indicators are perform-ing equally on ground except one indicator P1.4. Due to weighted sum approach used in AHP, obviously the final actual performance will tend to be more than passing performance. In this case the site gets Bronze Grade. Fuzzy-AHP has shown similar results without any overlap in the final performance of 3 scenarios (pessimistic, moderate, optimistic). Here important field knowledge is to be borne in mind. According to expert’s preference, the indicator P1.4 is least important and hence the performance difference of P1.4 is not much important to them, pro-vided there is a difference in performance in other Indicators. In this case the Fuzzy Reasoning Model have shown same results for both Actual and Passing. If expert feel this is a mistake then they have to modify the rule definition taking P1.4 variations into account. At this junc-ture, this assumed to be wrong result could be identified in advance from the sensitivity analy-sis (Chapter 5.4.2.3) that variation of P1.4 has not at all affected the output, hence here the results would be affected. Also from the Simulation it was found that P1.4 has contributed just 0.4% to final output. So in fuzzy reasoning model, we have better ways to understand the behaviour of the system in a more efficient manner without any real-life inputs.


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It is important to note here that for the Site-3 the result for AHP and other approaches are re-verse. This is due to the fact that while giving pairwise comparison matrices for Criteria the experts have considered the current condition of that area and assumed that Forest Manage-ment (FM) is more important than Area Management (AM) (Appendix-B; Table B.5). But in Fuzzy Reasoning Model we have considered the same rules for all the sites and in these rules (from % of contribution) we can say that AM is contributing (around 83%) much more that FM (around 17%). Hence a very important point here for the certifiers is that “Same rule can-not be applicable to all the sites”. It is necessary to have Expert rule for every site considering the respective ground condition and interactions. Since the preference order of site-1 and site-2 & site-4 have similarity with respect to the preference used by the expert rules, the outputs are in a comparable position, otherwise it would result in a very wrong evaluation.

Site-4 has another extreme condition, but here the extremity lies with the second most impor-tant Indicator. Here in AHP the site has achieved its performance as Silver grade, but in other approaches has lead to only Bronze. Getting Bronze seems to be rational for this site, because having one indicator performing well and others having performance as fair did not tell any extra-ordinary performance of the Forest management Unit and hence they are in reality not good enough to get Silver, which AHP has failed to say.

From the above discussion, it is clear that fuzzy-AHP has performed similar to AHP but can give the hint about the possible rank reversal danger in the output due to uncertainty in input preferences. On the other hand Fuzzy Reasoning Model has performed very efficiently in han-dling diverse data to accommodating uncertainty and expert rules. It is very important to note that the sensitivity & parameter analysis of the fuzzy reasoning model must be done before making the model available for final evaluation. Expert Rules have to be obtained with clear consciousness and it must be checked for consistency with cognitive mapping. Also the rela-tive percentage of contribution through simulation (using all possible combinations of input values) would provide a quick overview of most contributing and least contributing elements in the model apart from helping to arrange all the parameters according to their importance preference used in expert decision tree.


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6. Conclusions & Recommendation

The current certification system for assessing sustainability of forest management has prob-lems in input and in processing. In the input part the major problems are that a) the verifiers are of diverse nature and vaguely defined, b) experts assess the verifiers using verbal judge-ment but these judgements are considered as crisp number so judgement uncertainty is not considered and c) moreover on the ground verifiers are interrelated, but in the current system they are put under different hierarchical levels and hence their ground interaction reality is restricted. In the processing part a) Crisp numbers leads to under estimation or over-estimation, b) these numbers are processed using mathematical aggregation and hence uncon-trolled degree of compensation again leads to irrational interactions and information loss and c) interpretation of finally derived crisp number. These problems are put systematically as re-search questions and are analysed in the research to choose a proper approach and necessary procedures, which can lead us to the decisive solution and objective. Research Question 1: What sort of approach shall be used to transform the spatial and non-spatial data into a value judgement? First of all consider the diverse input as explicitly spatial element and overlay them in GIS environment. Then each record of these overlayed spatial elements can be converted into value judgement using Membership curves and linguistic classes defined by the experts. This can be either done in 2-tuple fuzzy linguistic approach or using Fuzzification function in Fuzzy-AHP or in Type-1 or Type-2 Fuzzy reasoning Model also. This is described as Path-3 in Figure 4.3. Currently most of the verifiers are considered as either implicitly spatial nature or non-spatial nature. If the LEI want to follow this way then consider all the input verifiers as non-spatial elements or implicitly spatial element, through ranking or rating or AHP or using advanced aggregation techniques and then convert them into value judgement as specified in the previ-ous paragraph. This prescription follows Path-1 and Path-2 of Figure 4.3. Two important options are to be borne in mind before converting the integrated data into a value judgement. In the First option, Expert can either apply their ground experience in bring-ing all the data into same comparable domain either by standardisation or normalisation and then they pass this standardised value to fuzzification function in Fuzzy Reasoning model to convert that quantity into a value judgement. In this case expert has to understand the nature of the verifier (cost or benefit), define possible input value ranges & its preferred range in order to convert them into a standardised value. In this way, since all the data are brought to same comparable level, the fuzzification functions and related linguistic classes for different pa-rameters at the same hierarchical level need not be different and hence analysing the fuzzy model for sensitivity would be very much in control. Otherwise in the Second Option, pass the raw data (non-standardised) directly into fuzzy reasoning model. But in this case for every pa-rameter the fuzzification function will vary, because it depends upon the characteristic of each parameter. Hence much effort is needed to incorporate the variations of value and its meaning with the membership classes and also this would not allow us to analyse the model efficiently.


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So understanding and providing solution to this first research question have solved the data diversity and uncertainty problems associated with the input part. Research Question 2: How shall the integration/process be done over value judgements? Once the data is converted into value judgement using membership function, they will have different strength of value judgement. These fuzzy value judgements can be processed using either any mathematical model like 2-tuple fuzzy linguistic approach or fuzzy-AHP or any inference mechanism. But using 2-tuple or fuzzy-AHP approach have not solved the compen-sation problem in hand. So Inference Mechanism is recommended, which needs expert ground knowledge as rules, for integrating value judgements. Research Question 3: How shall we use expert knowledge in the process? Expert knowledge on ground process can be utilised as a fuzzy rules for the inference. Since the number of rules increases tremendously with number of input parameters and number of linguistic classes, optimisation of rules is very important. Converting rules derived from expert into a Decision Tree instead of table would help to understand the clear logic behind the rules and also it will help the decision maker to trace back, if any flaw occurs. Also it is very important to note here that the process of building expert rules have eliminated the unwanted/redundant verifiers, which are mentioned in the definition. These rules also con-sider the inter-dependency of verifiers/indicators at different hierarchical level and hence the ground reality is implanted in the aggregation by using Expert Rules to confiscate compensa-tion. Expert rule can either be derived directly from the expert or through cognitive mapping approach, on either case the proper argumentation must be written down for future users to know the reason behind. Research Question 4: To what extent this fuzzy approach can improve the process with ref-erence to the existing system? Fuzzy reasoning model has helped the expert to include different level of his interpretational uncertainty for the value judgement and to understand the impact of this on the output. Also he can use his knowledge derived through years of experience on the ground processes as Fuzzy Rules. So using this approach diverse data can be handled, uncertainty in the input data, expert’s confidence & attitude are handled well than in other methods. Mathematical Compen-sation is avoided by using rule base along with proper compositional operators in the inference mechanism. Finally the output value can directly be represented as the Ecolabel classes instead of crisp numbers. So in overall, this approach has improved the evaluation process undoubt-edly. Research Question 5: How shall Sensitivity of the approach be measured? Sensitivity of the model is studied by varying the shape and slope of the membership curve. Also by varying the input values by small fraction, I have analysed its impact on the output.


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Also one can delete or add one parameter in the model and can check. But this is a special case in fuzzy model, because addition or deletion of any parameter completely alters the meaning of the fuzzy rules. So care must be taken in this analysis. But deletion of a parameter is possi-ble under certain conditions. For this, first convert the fuzzy rules into decision tree. In the de-cision tree the most important parameter comes first and least important parameter at the last. If we delete the least important item then it will not affect the decision tree. But if we delete any other parameter then the whole structure will have to be changed. So sensitivity analysis over number of parameter would require different sets of fuzzy rules, but it is very much pos-sible. In this research this part is not done, due to the non-availability of different sets of expert rules, but sensitivity in terms of shape, size and dimension (3-D in Type-2) has been tested/demonstrated in this research. It is found that the fuzzy logic approach is intelligently sensitive in a rational way. Also by using Cognitive Mapping, consistency of the expert knowledge can be checked and have provided quantitative information about ground interactions. Cognitive mapping has definitely gives the possibility of improving the quality of the process by providing mecha-nism to measure the in-consistency in expert rule and his mental map on ground interactions. More over by comparing with other existing methods like 2-tuple fuzzy linguistic approach or Fuzzy-AHP approach in terms of improved aggregation, incorporating ground interactions as expert rules and uncertainty, we can say that the quality of Fuzzy Reasoning Approach is much better than others. Overall this research has explored possible steps involved in building a proper methodology in order to provide a major direction to the current/future users in the path of sustainability as-sessment in forest management using fuzzy logic. Also this research can be utilised for any environmental domain. Recommendation: Since only small portion of the big hierarchy is considered for this research, immediate rec-ommendation is to study the feasibility of this approach over the whole hierarchy. Also exist-ing GIS softwares do not provide advanced approaches which are used in this research, hence development of dedicated decision support system is recommended/needed to include all the necessary components in a single interactive environment to make the evaluation process a uniform, transparent and with technically less effort from decision makers. So building Deci-sion Support System would enhance the full certification process in terms of repeatability, ef-ficiency and effectiveness.


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Agung F.P.M.W and A. Hinrichs (2000). Self-scoping Handbook for SNFM certifica-tion in Indonesia: Promotion of Sustainable Forest Management Systems in East Kalimantan (SFMP): GTZ in co-operation with Indonesian Ministry of Forestry.

Alan Purbawiyatna, (2002). Forest Certification as an evaluation process: The case study of Labanan Forest Management Unit, East Kalimantan – Indonesia. M.Sc. Thesis, International Institute for Geo-information and Earth Observa-tion (ITC), Enschede, The Netherlands.

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A-Xing Zhu, 1999. A personal construct-based knowledge acquisition process for natural resource mapping. Int. J. Geographical Information Science, Vol.13, No.2, 119-141.

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Appendix A-I: Description of LEI Indicators, Verifiers and its Intensity Scale INDICATOR DEFINITION VERIFIERS NORM (Intensity Scale)

P 1.1 Guarantee of Land utilization as a forest area

The guarantee of management unit area status re-land utiliza-tion, regional and Forest Utili-zation Management from the beginning until atleast for the duration of the venture which will provide security on the land being utilized. The com-munity, other land area users and other relevant agencies can see the boundary management as a form of effort in the con-tent of attaining recognition for the management unit area. Boundary poles are a form of signage “announcing” that the land area within carry legal obligations (entitlements)

1. Availability of Provincial

Land Use Plan (Rencana Tata Ru-ang Wilayah Propoinsi / RTRWP), forest Land Use (Tata Guna Hutan) and map of definitive land utiliza-tion in the Province/Regency Con-cerned

2. Level of compatibility and/or adjustment of management unit area status towards RTRWP, TGH and land utilization

3. Realization of delineation implementation

4. Quality of Boundary

• Excellent The management unit land area is assured a status fulfilling all legal requirements – the confirmation and forest delineation is acknowledged by the relevant government agencies and other sectors. Conditions of the boundary markings are good • Good The management area is assured a status fulfilling all legal aspects, however other users and government agencies do not acknowledge the confirmation and forest area delineation. Condition of boundary mark-ings is good. • Fair The management area is assured a status fulfilling all legal aspects, however other users and government agencies do not acknowledge the confirmation and forest area delineation. Conditions of boundary mark-ings are poor. • Poor The management area is assured a status fulfilling all legal aspects, however the confirmation and forest area delineation have not been completed. • Bad The management unit area does not fulfill all legal aspects.

P 1.2 Forest planning and use based on forest types and functions

The management unit area division according its allotment is based on physical character-istics of the land, which takes the form of watershed areas (DAS), Sea surface level, Slope, Land Sensitivity to Ero-sion and Rain Intensity. It is also known that forest types have various characteristics that need to be developed, so thereby produce forest classifications that will reflect on the prescriptions that need to be made by the management.

1. Delineation of protected and

production areas, according to land capability

2. Delineation of protected and production areas, according to for-est type and classification

3. Location/placement of pro-tected/conservation and production areas based on land capability and forest type

• Excellent Results on the area management will take into account the functions of the area that meet requirements as a protected and/or conservation area as well as take into consideration existing forest types and produce forest classifications. • Good Results on the area will consider the functions of the area that meet requirements as a protected and/or conservation area as well as take into consideration existing forest types, however do not produce forest classifications • Fair Results on the area management consider the functions of the area that meet requirements as a protected and/or conservation area and produce forest classifications, however they do not take into account existing forest types. • Poor Results on the area management consider the forest types and produce classifications, however they do not take into account the functions of the area that meet requirements for a protected or conservation area. • Bad Results on the area management does not consider the functions of the area that meet requirements as protected or conservation area as well as (other) forest types.


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P 1.3 The level of change in land cover due to en-croachment and conversion of for-est, fires, and other factors

Theft and other means of for-est clearing, change of forest function and other impedi-ments, including inappropriate management tactics can alter the form of (forest land) clo-sure. The scope of the form of closure can cause drastic changes on the forest types and ecological landscape.

1. Form and intensity of forest en-

croachment 2. Conversion of forest functions

and distribution of other rights 3. Intensity/frequency and scale of

forest fires that have occurred 4. Type of forest product mostly

lost 5. Form/type of disturbances to-

wards the forest and the inten-sity/frequency and scale of distur-bances

6. Over cutting

• Excellent No forest clearings and change of function, thefts, forest fires and other forms of impediments • Fair Forest type and function remains intact despite incidences of forest clearing, change of functions, thefts, fires and other impediments. Planned distribution of products can still be implemented. • Poor Due to forest clearing (skidding) and change of function, thefts, firest and others – the type of function of forest has changed and with it its planned distribution of products ( to be revised) • Bad All forest clearings, change of functions, thefts, fires etc. causes the change in the forest landscape – the corporate vision and mission (objective) has to be revised

P 1.4 A forest fire man-agement system

Forest fire is a natural disaster, which is a major drawback of tremendous proportions, how-ever its occurrence is unpre-dictable, making the readiness of a special task force (man-agement) essential in order to manage this well in the frame-work of prevention as well as containment.

1. Availability of skilled labor,

standard operational procedures (SOP), and equipment

2. Participation of local community and relevant institutions

3. Early warning system

• Good An organization is already in place that includes the community/relevant agencies, equipment including its early warning system, trained manpower and standard operating procedure (SOP to anticipate preven-tion and suppression of potential danger of forest fires) • Fair An organization in place including community/relevant agencies, equipment and its early warning system, and trained manpower, however no SOP to anticipate prevention and suppression measures. • Poor An organization in place including community/relevant agencies, equipment and its early warning system, trained manpower and a SOP to do preventive and suppressive measures but they are inadequate • Bad No organization, equipment and trained manpower in place to anticipate dangers of forest fires.

P 1.5 The selection and implementation of silvicultural sys-tems in compliance with the local for-est ecosystems

Selection, planning, determin-ing and the application of a silviculture system in compli-ance with force of area support, the forest and its ecosystem

1. Forest Ecosystem data 2. Stands Structure 3. Type composition 4. Tree type regeneration data 5. Implementation of each level of

activity from the silviculture system applied

• Excellent Silviculture system is in line with the local ecosystem that is determined based on updated data and maps and is applied in a correct manner • Fair Silviculture system is determined and applied accordingly to current operating regulation • Poor Incorrect application of chosen silviculture system • Bad No effort in choosing or applying a silviculture system that is in line with the local system

P 1.6 Maintenance of a variety of non-timber forest prod-ucts in guaranteed

The existence and potential of non-timber products provide continuous prospects and guar-antee of a good forest.

1. Number and Types of non-timber products

• Excellent The prospects for non-timber products are known and can be sustained • Fair Prospects of non-timber products only partly known and can be sustained • Poor Prospects of non-timber products are known but cannot be sustained • Bad Prospects of non-timber products are not known


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Appendix A-II : Verifiers Preferred by Experts & their possible Standardization Procedure

MEASUREMENT

STANDARDISATION VARIABLES

INDICATOR

VERIFIERS CONSIDERED

(Choice of the Experts in accordance with Norms)

DATA TYPE

EFFECT

MIN

MAX

PREFERRED

STANDARDISATION EQUATION

1. Stake Holder’s Agreement

NOMINAL (converted to Interval)

BENEFIT No

Agreement (0%)

Complete Agreement

(100%)

More than 90% Agreement

2. Legal Fulfilment

NOMINAL (converted to Interval)

BENEFIT Not

fulfilled (0%)

Completely fulfilled (100%)

More than 90% Agreement

3a. Realization of Boundary delineation & implementation

RATIO BENEFIT 0 m Maximum Boundary

Perimeter (m)

More than 90% of its full length

Output = 0 if x <= 60% = (x-60) * 100 / (90-60) if 60% < x < 90% = 1 if x >= 90%

P 1.1 Guarantee of Land utilization as a for-est area

3b. Quality of Boundary

NOMINAL BENEFIT Bad Good Fair, Good

Output = Verbal Judgment (Bad,Fair,Good)

1. Delineation of protected and production areas, accord-ing to land capability

INTERVAL (spatial)

BENEFIT 0% 100% Match More than 80%

2. Delineation of protected and production areas, accord-ing to forest type and classifi-cation

INTERVAL (spatial)

BENEFIT 0% 100% Match More than 80%

P 1.2 Forest planning and use based on forest types and functions

3.Location/placement of pro-tected /conservation and pro-duction areas based on land capability and forest type (Implementation)

INTERVAL (spatial)

BENEFIT 0% 100%

Implemented More than 80%

Spatial Overlay Analysis Output = 0 if x <= 40% = (x-40) * 100 / (80-40) if 40% < x < 80% = 1 if x >= 80%

(Chapter 4, Fig.4.6)


89

1. Intensity of Forest Fire

RATIO (converted

to NOMINAL)

COST 0 trees 1 year Production

0 to 10% of 1 year production

2. Forest encroachment

RATIO (converted

to NOMINAL)



3. Other disturbances due to disease, flood, etc.

RATIO (converted

to NOMINAL)



P 1.3

The level of change in land cover due to en-croachment and conversion of for-est, fires, and other factors

4. Over cutting

RATIO (converted

to NOMINAL)



Output = Verbal Judgment (Low = 0 to 10% of 1 year production Moderate = 10% to 50% of 1 year production High = > 50% of 1 year production)

1. Availability & Level of Early Warning System

NOMINAL BENEFIT Low High High Output = Verbal Judgment (Low, Moderate, High)

2. Community & Institutional Participation

NOMINAL BENEFIT Low High High Output = Verbal Judgment (Low, Moderate, High)

P 1.4 A forest fire man-agement system

3. Availability of Skilled La-bour

NOMINAL BENEFIT Bad Good Fair, Good Output = Verbal Judgment (Bad, Fair, Good)

1. Level of Silviculture Im-plementation

INTERVAL (spatial)

BENEFIT 0% 100% Imple-

mented More than 80%


2. Compliance of local forest eco system and silviculture system plan

INTERVAL (spatial)

BENEFIT 0% 100% Com-

pliance More than 80%


P 1.5 The selection and implementation of silvicultural sys-tems in compliance with the local for-est ecosystems 3. Level of Stand Structure,

Species composition & Re-generation (Status Maps)

NOMINAL

(ground check)

BENEFIT Bad Good Fair, Good Output = Verbal Judgment (Bad, Fair, Good)


90

1. Availability of different type of Non-Timber Forest Products (NTFP)

RATIO (ground check –

Converted to NOMI-

NAL)

BENEFIT 0

(BAD)

Maximum Possible

(from His-trorical re-

cords)in that Locality (GOOD)

Fair, Good

P.1.6 Maintenance of a variety of non-timber forest prod-ucts in guaranteed

2. Knowledge of Potential extraction/utilisation status of NTFP (each type)

NOMINAL BENEFIT Bad Good Fair, Good

Output = Verbal Judgment (Bad, Fair, Good)


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APPENDIX B: Input data sets for AHP approach used in current LEI system Very first step in AHP is providing Pairwise Comparison Matrix (PCM). In LEI, expert has to provide PCM at different levels. Every indicator is defined descriptively (Appendix A-I) that it can be attributed with any one of the five possible norms/alternatives: Excellent, Good, Fair, Poor and Bad, with reference to fulfilment of certain conditions. In order to assess every indicator’s performance, Experts are requested to provide pairwise comparison matrix (PCM), in which they compare every possible norm with respect to each other using certain ‘verbal importance scale’ as mentioned in Chapter 3, Table 3.2. This needs the field check information and their experience in comparing the ground situation for achieving the reason-able level of qualification of that indicator in hand. For example if the expert compares the norms ‘Excellent’ with ‘Bad’ and says ‘Strongly More Valuable’ it means that “Achieving ‘Excellent’, as the performance of the Indicator, is Strongly More Valuable than Achieving ‘Bad’ (really meaning that Stronger efforts are needed on the ground to achieve Excellent from Bad). Suppose while comparing ‘Good’ with

P1.1 Excellent Good Fair Poor Bad

Excellent Equally valuable

Equally to Weakly more valuable


Moderately to strongly more valuable

Strongly More valuable

Good Equally valuable Equally Valu-able

Weakly more valuable

Weakly to moderately more valuable

Fair Equally Valu-able

Weakly more valuable

Weakly to moderately more valuable

Poor equally valuable


Bad Equally valu-able

Table B.1a: The Original Verbal Pairwise Comparison Expected from Experts

P1.1 Excellent Good Fair Poor Bad

Excellent 1 2 2 6 7 Good 1 1 3 4 Fair 1 3 4 Poor 1 2 Bad 1

Table B.1b: Numerically converted Pairwise Comparison Matrix


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‘Fair’ if he says ‘Equally Valuable’ which means that “Achieving Good is Equally considered as achieving Fair’ (indirectly it reflects that on the ground getting Good performance needs same effort as achieving Fair). This is the original way the PCM is provided by Expert using verbal scale. Verbal PCM for the Indicator P1.1 of Site-1 is provided in the Table B.1a. This Verbal comparison is transformed into a numeric scale for analysis purpose, as specified in Table B.1b. The empty cells can be deduced by putting the inverse of the diagonally opposite cell inputs/values. The presence of value 3.5 in Table3.2 (in P1.1) is not explainable, since these matrices are given by experts of LEI, Bogor, Indonesia. The numeric pairwise Comparison Matrix thus obtained for the Site 1 as a test data are repre-sented in an optimised way in the Table B.2.

From these matrices we can find out the relative performance of each of the norm under each indicator. There are many ways of finding relative weights (Sharifi, 2002). In this research we have considered the Column Sum approach (Table B.3a). The first step (step1) in finding the

AREA MANAGEMENT P1.1 Good Fair Poor Bad P1.2 Good Fair Poor Bad Excellent 2 2 6 7 Excellent 2 3 5 6 Good 1 3 3.5 Good 3 4 5 Fair 3 3.5 Fair 2 3 Poor 2 Poor 2 P1.3 Fair Poor Bad P1.4 Fair Poor Bad Excellent 2 3 5 Good 1 1 2 Fair 2 4 Fair 1 2 Poor 3 Poor 2 FOREST MANAGEMENT P1.5 Fair Poor Bad P1.6 Fair Poor Bad Excellent 1 2 4 Excellent 1 2 3 Fair 2 4 Fair 2 3 Poor 2 Poor 2

FOREST RESOURCES SUSTAINABILITY AM p1.2 p1.3 p1.4 FM p1.5 p1.6 p1.1 5 3 7 p1.5 1 4 p1.2 0.5 3 p1.6 1 p1.3 5 FRS FM AM 2

Table B.2: The Pairwise Comparison Matrix for Each Indicator for Site 1


93

relative weight in this approach is to calculate the sum of each column of a given pairwise comparison matrix. Next step (step2) is normalizing each element in the PCM by dividing them with the column sum and add the resultant elements in each row. Finally (step 3) divide this row sum by number of elements used in the pairwise comparison matrix. This will give performance of each element. Also instead of dividing by number of elements as said in step3, If we divide the row sum with the maximum occurrence value then we will get the relative performance. Though both reflects the same meaning, LEI considers the relative per-formance values. Both the performance & relative performance values are given in the Table B.3. For Area Management (AM) and Forest Management (FM), the performance obtained has the share from its upper hierarchy, that is Forest Resources Sustainability (FRS), hence we have to multiply performance values of AM & FM by the corresponding performance values at FRS level (which is reflected in the FRS share column). Before accepting this relative performance, these matrices are to be checked for Consistency. Consistency Check helps us to find out how consistent the judgment of the expert is, while providing pairwise comparison matrix. First Step for checking the Consistency is to multiply each column total (of pairwise comparison matrix) for a particular Indicator by the calculated Relative Performance (Rel. Perf.) of that Indicator and add the resultant values. Next we have to subtract the number of elements (Norms considered i.e., 5 for P1.1) from the result of ear-lier step. Finally divide the result of 2nd step by the number of norms less one (4 for P1.1). The resultant value indicates the percentage of Consistency for the given matrix. If this value is less than 0.1 that is 10% then the matrix can be considered as Consistent, otherwise we have to check the problematic point. Once the consistency is obtained we can use these rela-tive performance values for further aggregation. Similarly we can calculate for all other test sites. The test data used for Site-2, Site-3 and Site-4 are as given in Table B.4, B.5, B.6. Original Normalised

P1.1 Excellent Good Fair Poor Bad P1.1 Excellent Good Fair Poor Bad

Excellent 1 2 2 6 7 Excellent 0.43299 0.433 0.433 0.444 0.412

Good 0.5 1 1 3 3.5 Good 0.21649 0.216 0.216 0.222 0.206

Fair 0.5 1 1 3 3.5 Fair 0.21649 0.216 0.216 0.222 0.206

Poor 0.1667 0.333 0.3333 1 2 Poor 0.07216 0.072 0.072 0.074 0.118

Bad 0.1429 0.286 0.2857 0.5 1 Bad 0.06186 0.062 0.062 0.037 0.059

columnsum 2.3095 4.619 4.619 13.5 17

Performance

P1.1 rowsum rowsum/5 Rel.Perf.

Excellent 2.1552 0.431036 1

Good 1.0776 0.215518 0.5

Fair 1.0776 0.215518 0.5

Poor 0.4082 0.081643 0.18941

Bad 0.2814 0.056286 0.13058

Table B.3a: Performance Calculation (for Indicator P1.1 of Site-1)


94

P1.1 Performance Rel.Perf. P1.2 Performance Rel.Perf. Excellent 0.431 1.0000 Excellent 0.4238 1.0000 Good 0.2155 0.5000 Good 0.2977 0.7025 Fair 0.2155 0.5000 Fair 0.1408 0.3321 Poor 0.0816 0.1894 Poor 0.0837 0.1975 Bad 0.0563 0.1306 Bad 0.0540 0.1274 P1.3 Performance Rel.Perf. P1.4 Performance Rel.Perf. Excellent 0.4709 1.0000 Good 0.2857 1 Fair 0.2840 0.6032 Fair 0.2857 1 Poor 0.1715 0.3642 Poor 0.2857 1 Bad 0.0736 0.1564 Bad 0.1429 0.5 P1.6 Performance Rel.Perf. P1.5 Performance Rel.Perf. Excellent 0.3507 1.0000 Excellent 0.3636 1 Fair 0.3507 1.0000 Fair 0.3636 1 Poor 0.1893 0.5396 Poor 0.1818 0.5 Bad 0.1093 0.3117 Bad 0.0909 0.25 PM Weight P1.5 0.8 AM Weight P1.6 0.2 P1.1 0.5681 P1.2 0.1333 FRS Weight P1.3 0.2410 AM 0.6667 P1.4 0.0576 PM 0.3333

Excellent Good Fair Poor Bad 0.5681 P1.1 1.0000 0.5000 0.5000 0.1894 0.1306 0.6667 AM 0.1333 P1.2 1.0000 0.7025 0.3321 0.1975 0.1274

0.241 P1.3 1.0000 - 0.6032 0.3642 0.1564 FRS 0.0576 P1.4 - 1.0000 1.0000 1.0000 0.5000

0.8 P1.5 1.0000 - 1.0000 0.5000 0.2500 0.3333 FM 0.2 P1.6 1.0000 - 1.0000 0.5396 0.3117

Table B.3: Relative Performance of Each Norm under Each Indicator for Site-1


95

site2 AREA MANAGEMENT P1.1 Good Fair Poor Bad P1.2 Good Fair Poor Bad Excellent 3 5 7 9 Excellent 2 3 7 9 Good 2 5 7 Good 2 5 7 Fair 3 5 Fair 4 6 Poor 3 Poor 3 P1.3 Fair Poor Bad P1.4 Fair Poor Bad

Excellent 3 6 9 Good 2 3 7 Fair 3 6 Fair 2 5 Poor 3 Poor 4 FOREST MANAGEMENT P1.5 Fair Poor Bad P1.6 Fair Poor Bad Excellent 5 7 9 Excellent 4 6 9 Fair 3 4 Fair 5 6 Poor 2 Poor 2 FOREST RESOURCES SUSTAINABILITY AM p1.2 p1.3 p1.4 FM p1.5 p1.6 p1.1 2.6 2.5 2.4 p1.5 1 1.5 p1.2 1.5 1.7 p1.6 1 p1.3 1.5 FRS FM AM 3 Excellent Good Fair Poor Bad 0.4487 P1.1 1.0000 0.4752 0.2804 0.1337 0.0687 0.75 AM 0.2257 P1.2 1.0000 0.6176 0.4092 0.1500 0.0785 0.1807 P1.3 1.0000 - 0.4421 0.1846 0.0815

FRS 0.1449 P1.4 - 1.0000 0.5868 0.3607 0.1162 0.6 P1.5 1.0000 - 0.3057 0.1378 0.0842 0.25 FM 0.4 P1.6 1.0000 - 0.4552 0.1418 0.0838

Table B.4: Pairwise Comparision Matrices, Relative Performance & Weights for Site-2


96

site3 AREA MANAGEMENT P1.1 Good Fair Poor Bad P1.2 Good Fair Poor Bad Excellent 2 2 3 4 Excellent 1 2 2 4 Good 1 2 3 Good 2 2 4 Fair 2 3 Fair 1 2 Poor 2 Poor 2 P1.3 Fair Poor Bad P1.4 Fair Poor Bad Excellent 1 2 4 Good 1 1 1

Fair 2 4 Fair 1 1 Poor 2 Poor 1 FOREST MANAGEMENT P1.5 Fair Poor Bad P1.6 Fair Poor Bad Excellent 1 2 3 Excellent 1 2 2 Fair 2 3 Fair 2 2 Poor 2 Poor 1

FOREST RESOURCES SUSTAINABILITY AM p1.2 p1.3 p1.4 FM p1.5 p1.6 p1.1 0.5 0.25 1 p1.5 1 2 p1.2 0.5 2 p1.6 1 p1.3 4 FRS FM AM 0.5 Excellent Good Fair Poor Bad

0.125 P1.1 1.0000 0.5724 0.5724 0.3239 0.1975

0.3333 AM 0.25 P1.2 1.0000 1.0000 0.5000 0.5000 0.2500 0.5 P1.3 1.0000 - 1.0000 0.5000 0.2500

FRS 0.125 P1.4 - 1.0000 1.0000 1.0000 1.0000 0.6667 P1.5 1.0000 - 1.0000 0.5396 0.3117 0.6667 FM 0.3333 P1.6 1.0000 - 1.0000 0.5000 0.5000



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site4 AREA MANAGEMENT P1.1 Good Fair Poor Bad P1.2 Good Fair Poor Bad Excellent 2 4 6 8 Excellent 2 4 5 7 Good 3 4 5 Good 3 4 5 Fair 2 3 Fair 2 3 Poor 2 Poor 2 P1.3 Fair Poor Bad P1.4 Fair Poor Bad Excellent 3 6 7 Good 3 5 6 Fair 3 5 Fair 2 4

Poor 2 Poor 2 FOREST MANAGEMENT

P1.5 Fair Poor Bad P1.6 Fair Poor Bad Excellent 3 6 7 Excellent 3 5 7 Fair 2 4 Fair 2 3 Poor 2 Poor 2

FOREST RESOURCES SUSTAINABILITY

AM p1.2 p1.3 p1.4 FM p1.5 p1.6 p1.1 2 4 6 p1.5 1 4 p1.2 4 5 p1.6 1 p1.3 2

FRS FM AM 2

Excellent Good Fair Poor Bad 0.4878 P1.1 1.0000 0.6027 0.2695 0.1642 0.1034 0.6667 AM 0.3322 P1.2 1.0000 0.6408 0.2880 0.1821 0.1132 0.1128 P1.3 1.0000 - 0.4425 0.1698 0.1029

FRS 0.0672 P1.4 - 1.0000 0.4516 0.1748 0.1063 0.8 P1.5 1.0000 - 0.3835 0.1918 0.1112 0.3333 FM 0.2 P1.6 1.0000 - 0.3719 0.2109 0.1237



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APPENDIX C-I : Detailed Modified Methodology of FUZZY-AHP

This fuzzy AHP approach is the hybrid synthesis of many concepts like AHP, fuzzy set the-ory, fuzzy extent analysis, alpha-cut analysis, Topsis ideal solution method and vector match-ing functions. In this approach first of all the Decision Maker (DM) has to provide the normal pairwise comparison matrix (PCM) as it is done for AHP, which is consistent (Step 1). Num-ber of PCM depends on the number of Criteria. If the user has 4 criteria then number of PCM required is 5, because for each criterion DM has to compare all the alternatives leading to 4 PCM + one PCM for comparing all criteria amongst themselves. The PCMs used for the cur-rent research are given in Appendix-B. In the second step (step 2), this crisp PCM is con-verted into fuzzy range using a pre-defined fuzzy triangular function and the membership values of all the element within this range will be calculated as defined below:

Where a1,a2,a3 are the Left, Middle and Right base points of a linguistic triangle and a2 cor-responds to the given crisp value in PCM. The range [a1,a2,a3] represent the fuzzy uncertain range of the decision makers judgment. The crisp PCM now becomes Fuzzy PCM (FPCM).

The different fuzzy ranges for different values of PCM are as mentioned in the table below.

Input Crisp Value Output Fuzzified Values 1 (1,1,1) if Diagonal

(1,1,3) otherwise * 3 (1,3,5) 5 (3,5,7) 7 (5,7,9) 9 (7,9,11)

Table C.1:Fuzzy Pairwise Conversion Let PCM is considered as x . If x > 1 then fuzzified output is (x-2),x,(x+2)

(x-a1)/(a2-a1) when a1 ��x��a2

µA(x) = (a3-x)/(a3-a2) when a2 ��x��a3 Eqn. (C.1.1)

0 otherwise

[ã11l ã11m ã11r] [ã12l ã12m ã12r] …………………[ã1nl, ã1nm, ã1nr] [ã21l ã21m ã21r] [ã22l ã22m ã22r] …………………[ã2nl, ã2nm, ã2nr] [ã31l ã31m ã31r] [ã32l ã12m ã32r] …………………[ã3nl, ã3nm, ã3nr]

FPCM = : : : : : Eqn.(C.1.2)

: : : : :

[ãm1l ãm1m ãm1r] [ãm2l ãm2m ãm2r] ……………[ãmnl, ãmnm, ã1nr]


99

Inverse of Input Crisp Value Output Fuzzified Values 1/1 (1/1 1/1, 1/1) If Diagonal

(1/3,1,1) otherwise * 1/2 (1/4, 1/2, 1/1) * 1/3 (1/5, 1/3, 1/1) 1/5 (1/7, 1/5, 1/3) 1/7 (1/9, 1/7, 1/5) 1/9 (1/11, 1/9, 1/7)

TableC.2: Reciprocal Fuzzy Pairwise Conversion * presents the modification made in the fuzzification functions. Since when we compare an object or parameter with itself by any means we don’t make any uncertain assumption. They are always equal. So in the diagonal elements of PCM, the value must be always one even after fuzzification, which was not considered in the Hepu Deng approach. Also when input value is 1/2, then the fuzzified values will be 1/4,1/2,1/0. In that case last value becomes in-finity, so it is modified that when input is 1/2, the fuzzified values will be 1/4,1/2,1/1.

The extended fuzzy arithmetic over two different fuzzy pairwise comparison elements is de-fined as followed:

Input Operation Output A+B (a1+b1 , a2+b2, a3+b3) A-B (a1-b3, a2-b2, a3-b1) A*B (a1*b1, a2*b2, a3*b3) A/B (a1/b3, a2/b2, a3/b1) Inverse(A) (1/a3, 1/a2,1/a1) Inverse(B) (1/b3, 1/b2, 1/b1)

TableC.3: Fuzzy Arithmetic Once these ranges are fixed, the next step (step 3) is to find out the performance ratings of each of the alternative with respect to all criteria. This is done by fuzzy extent analysis as

Σ ãj j=1 to q

Wj = = [xi(l) xi(m) xi(r) ]

Σ Σ ãij Eqn.(C.1.3) i =1 to p j =1 to q Where p – number of rows ; q – number of columns in the choosen PCM l - possible performance value in Left extreme m – possible performance value in Middle Range r – Possible performance value in Right extreme


100

Once each of the elements in FPCM are converted into performance rating, we have to multi-ply these performance ratings by the criterion weights (step 4) which is also obtained using the same manner as said above. Now we have uncertain range of values over which any value can be considered as performance value and hence DM is asked to say about his confi-dence about his judgement (step 5). His confidence value (α = [0,1]) will help us to choose the range of uncertainty from ALPHA-CUT approach (Fig. C.1). When α=1, the DM is very sure about his judgement and in this case the FPCM is reduced to crisp PCM. When α=0, the uncertainty is maximum and hence the full fuzzy range is considered.

Alpha-cut analysis have further restricted our circumference of uncertain range (Zα)

Figure C.1: Alpha_Cut Example

[Zα11(l) , Zα

11(r)] [Zα12(l) , Zα

12(r)] [Zα13(l) , Zα

13(r)]……….[Zα1n(l) , Zα

1n(r)] [Zα

21(l) , Zα21(r)] [Zα

22(l) , Zα22(r)] [Zα

23(l) , Zα23(r)]……….[Zα

2n(l) , Zα2n(r)]

[Zα31(l) , Zα

31(r)] [Zα32(l) , Zα

32(r)] [Zα33(l) , Zα

33(r)]……….[Zα3n(l) , Zα

3n(r)] : : : :

Zα = : : : : Eqn.(C.1.4)

: : : : : : : : [Zα

m1(l) , Zαm1(r)] [Zα

m2(l) , Zαm2(r)] [Zα

m3(l) , Zαm3(r)]……….[Zα

mn(l) , Zαmn(r)]


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Now DM’s attitude plays a role in deciding the performance value. Since we have still certain range of possible values for performance, we have to choose one value which either may be lowest value or highest value or middle value as per DM’s atttitude of pessimistic, optimistic or middle respectively. This is done by asking Optimism Index (λ) value which take 0 to 1. When he is pessimistic λ=0, the lowest value is taken and when he is optimistic, λ=1, highest value is taken. Using the value of λ (Step 6), we can again convert the fuzzy range into a crisp range using following equation

Using above equation all values of alpha-cut matrix are converted into crisp performance matrix(CPM).

Next step (Step 7) is to do normalisation process to obtain the normalised performance matrix. Normalisation is done by dividing all the elements in CPM by square root of sum of square of all the elements in CPM. The resultant normalised matrix (NPM) is as follows.

Now the selection is done by identifying the similarity measurement from best possible and worst possible alternative scores for all criteria (Step 8). The best possible score is a vector

Zα λ = λ * Zα

ij(r) + (1-λ) * Zα ij(l) where λ∈[0,1] Eqn.(C.1.5)

Where Zα

ij(r) refers to the right most value obtained from α- cut analysis Zα

ij(r) refers to the left most value

Zλ’

11α Zλ’12α Zλ’

13α ……….Zλ’1nα

Zλ’21α Zλ’

22α Zλ’23α ……….Zλ’

2nα Zλ’

31α Zλ’32α Zλ’

33α ……….Zλ’3nα

Zλ’α = : : : : Eqn.(C.1.6)

: : : : : : : : Zλ’

m1α Zλ’m2α Zλ’

m3α ……….Zλ’mnα

Zλ

11α Zλ12α Zλ

13α ……….Zλ1nα

Zλ21α Zλ

22α Zλ23α ……….Zλ

2nα Zλ

31α Zλ32α Zλ

33α ……….Zλ3nα

Zλα = : : : : Eqn.(C.1.7)

: : : : : : : : Zλ

m1α Zλm2α Zλ

m3α ……….Zλmnα


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which contains highest scores in each criteria and worst possible score is another vector which contains lowest scores in each criteria out of all available alternatives. From this we can find out the degree of similarity (Step 9) between each alternative by using

Vector matching function as follows.

At this juncture, instead of Vector Matching function one can also use Ideal Position method. In this method the Distances of Actual and Passing performance vectors will be calculated from the Ideal Positive (best possible score) and Ideal negative (worst possible score) vectors and final performance indicates that how far the performance is away from the negative ideal vector. More the distance from the negative ideal vector then it will lead to good performance. The alternative which has the highest final performance index value (Step 10) will be considered as the best choice in both the functions. Here one can vary the values of Alpha (α) & Lamda (λ) between 0 to 1 to see different scenario like “optimistic or pessimistic view”, “highly uncertain or less uncertain” and can find out the variation of final performance index value. If there is a rank reversal at many points then attentions must be given to check the consistency of the input crisp pairwise comparision matrix. Also one can vary the predefined Triangular Uncertainty base and can model the variations.

Best Possible Score Aλ+α = (zλ+

1α, zλ+2α, zλ+

2α, zλ+2α,....... zλ+

nα) Worst Possible Score Aλ -

α = (zλ-1α, zλ-

2α, zλ-2α, zλ-

2α,....... zλ-nα)

Where zλ+

1α = max(zλ1jα , zλ

2jα , zλ3jα ,………. zλ

mjα ) zλ-

1α = min(zλ1jα , zλ

2jα , zλ3jα ,……….. zλ

mjα )

Aλiα Aλ+

α Sλ+

iα = --------------------------------- Eqn.(C.1.8) Max(Aλ

iα Aλiα, Aλ+

α Aλ+α)

Aλ

iα Aλ -α

Sλ -iα = --------------------------------- Eqn.(C.1.9)

Max(Aλiα Aλ

iα, Aλ -α Aλ -

α)

Where Aλ

iα = (Zλi1α Zλ

i2α Zλi3α ……….Zλ

inα) (i th row of overall performance matrix, i = 1 to m) Sλ+

iα Final Performance Index Pλ

α i = ---------------- Eqn.(C.1.10) (Sλ+

iα + Sλ -iα)


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APPENDIX C-II: Step By Step Execution Of Fuzzy Ahp In fuzzy AHP first step is to convert the input crisp pariwise comparision matrix (PCM) into fuzzy PCM. Table C.4 shows the conversion of PCM of Indicator P1.1 from Site-1 data set, into a fuzzy PCM and respective performance values using both crisp and fuzzy PCM. Step1, Step2 and Step3 as specified in Chapter 4.3.1 is done till now. Step-1 is acquiring crisp PCM. Step-2 is converting Crisp PCM into Fuzzy PCM. Step-3 is performance calculation. In Step-3, for Calculating the Fuzzy Performance values, fuzzy ex-tent analysis is used as specified in the Equation C.1.3 under Appendix C-I. As an example, the following process explains the process involved in fuzzy extent analysis for calculating fuzzy performance values of 1st Row (for Excellent Alternative) in Indicator P1.1 under Site-1 data: Total sum of the whole fuzzy PCM = (1+1+1+4+5+0.25+1+1+1+1.5+0.25+1+1+1+1.5+0.125+0.2+0.2+1+1+0.111+0.1818+0.1818+0.25+1), (1+2+2+6+7+0.5+1+1+3+3.5+0.5+1+1+3+3.5+0.1667+0.333+0.333+1+2+0.1428+0.2857+0.2857+0.5+1) (1+4+4+8+9+1+1+3+5+5.5+1+3+1+5+5.5+0.25+1+1+1+4+0.2+0.6667+0.6667+1+1)

= (25.7496, 42.0469, 67.7834) = (a1,a2,a3)

The first row sum (for Excellent)= (1+1+1+4+5), (1+2+2+6+7),(1+4+4+8+9)

= (12,18,26) = (b1,b2,b3) First row sum / Total sum = (a1,a2,a3)/(b1,b2,b3) = (a1/b3, a2/b2, a3/b1)

= (12/67.7834, 18/42.0469, 26/25.7496) = (0.177703, 0.42809, 1.0097)

This can be checked in the Table C.4. Similarly we can calculated for all other rows and all other indicators. Table C.5 completely sketches the performances of all Indicators and rela-tive weightages over hierarchy for Site-1 Data. Once we have calculated the Performance values and weights, we can ask the experts to chose the performance value according to the ground condition & field check inputs. Table C.6 shows the performance chosen by the Expert and alpha_cut values applied over it. Once the performance of each indicator is chosen, then we can proceed ahead with all the steps to find the final performance values of “Actual” and “Passing”..


104

CRISP PERFORMANCE 1 2 2 6 7 0.431 Step 1 0.5 1 1 3 3.5 0.2155 P11 = 0.5 1 1 3 3.5 0.2155 0.1667 0.3333 0.3333 1 2 0.0816 0.1429 0.2857 0.2857 0.5 1 0.0563 Step 3 FUZZY PERFORMANCE (1,1,1) (1,2,4) (1,2,4) (4,6,8) (5,7,9) Excellent 0.17703 0.42809 1.0097

Step 2 (0.25,0.5,1) (1,1,1) (1,1,3) (1,3,5) (1.5,3.5,5.5) Good 0.070076 0.21404 0.60195

fuzzy_P11 = (0.25,0.5,1) (1,1,3) (1,1,1) (1,3,5) (1.5,3.5,5.5) Fair 0.070076 0.21404 0.60195

(0.125,0.16667,0.25) (0.2,0.33333,1) (0.2,0.33333,1) (1,1,1) (1,2,4) Poor 0.037251 0.091166 0.28156

(0.11111,0.14286,0.2) (0.1818,0.2857,0.6667) (0.1818,0.2857,0.6667) (0.25,0.5,1) (1,1,1) Bad 0.025445 0.052661 0.13722 Table C.4 : Fuzzified Pairwise Comparison Matrix of Indicator P1.1 (Site-1 Data)


105

a) SITE1 - FUZZY PERFORMANCE VALUES OF ALL INDICATORS Excellent Good Fair Poor Bad P1.1 0.1770 0.4281 1.0097 0.0701 0.2140 0.6019 0.0701 0.2140 0.6019 0.0373 0.0912 0.2816 0.0254 0.0527 0.1372 P1.2 0.1483 0.3925 1.0029 0.1075 0.3117 0.8023 0.0504 0.1539 0.4814 0.0380 0.0912 0.2741 0.0255 0.0508 0.1438 P1.3 0.1506 0.4380 1.1964 - 0.1067 0.2986 0.8445 0.0615 0.1924 0.5630 0.0379 0.0710 0.1994 P1.4 - 0.1081 0.2857 0.8000 0.1081 0.2857 0.8000 0.1081 0.2857 0.8000 0.0473 0.1429 0.2909 P1.5 0.1316 0.3636 0.9941 - 0.1316 0.3636 0.9941 0.0658 0.1818 0.4970 0.0417 0.0909 0.2130 P1.6 0.1081 0.3471 1.0700 - 0.1081 0.3471 1.0700 0.0676 0.1983 0.5761 0.0446 0.1074 0.3292 b) FUZZY AHP HIERARCHICAL WEIGHTAGES WEIGHTS

WEIGHTS 0.2229 0.5210 1.1550 P1.1 0.2857 0.6667 1.5385 AM 0.0533 0.1530 0.3850 P1.2 0.1159 0.2714 0.6825 P1.3 FRS 0.0324 0.0546 0.1330 P1.4 0.3529 0.8000 1.6800 P1.5 0.1786 0.3333 0.6154 FM 0.1373 0.2000 0.3600 P1.6

Table C.5 : Fuzzy Performance values & (Modified)Fuzzy-AHP Hierarchical weights ( Site-1 Data)


106

FOR SITE 1 Area Management Forest Management P1.1 P1.2 P.13 P1.4 P1.5 P1.6

(Poor) (Good) (Fair) (Fair) (Fair) (Fair) Qualitative (Fair) (Fair) (Fair) (Poor) (Fair) (Fair)

0.0373 0.0912 0.2816 0.1075 0.3117 0.8023 0.1067 0.2986 0.8445 0.1081 0.2857 0.8000 0.1316 0.3636 0.9941 0.1081 0.3471 1.0700 fuzzy performance 0.0701 0.2140 0.6019 0.0504 0.1539 0.4814 0.1067 0.2986 0.8445 0.1081 0.2857 0.8000 0.1316 0.3636 0.9941 0.1081 0.3471 1.0700

0.0024,0.0317,0.5003 0.0016,0.0318,0.4752 0.0035,0.054,0.8868 0.001,0.0104,0.1637 0.0083,0.097,1.0277 0.0026,0.0231,0.237 weighted performance 0.0045,0.0743,1.0697 0.0008,0.0157,0.2851 0.0035,0.054,0.8868 0.001,0.0104,0.1637 0.0083,0.097,1.0277 0.0026,0.0231,0.237

alpha_cut [0.017,0.266] [0.0167,0.2535] [0.0288,0.4704] [0.0057,0.087] [0.0526,0.5623] [0.0129,0.1301] (with 50% confidence) [0.0394,0.572] [0.0082,0.1504] [0.0288,0.4704] [0.0057,0.087] [0.0526,0.5623] [0.0129,0.1301]

Lamda_function 0.1415 0.1351 0.2496 0.0464 0.3075 0.0715

( Moderate attitude) 0.3057 0.0793 0.2496 0.0464 0.3075 0.0715

Normalised 0.4201 0.8624 0.7071 0.7071 0.7071 0.7071

0.9075 0.5063 0.7071 0.7071 0.7071 0.7071

Positive_Ideal_Vector 0.9075 0.8624 0.7071 0.7071 0.7071 0.7071

Negative_Ideal_Vector 0.4201 0.5063 0.7071 0.7071 0.7071 0.7071

Positive_Similarity 0.4629 1 1 1 1 1 1 0.5871 1 1 1 1

Negative_Similarity 1 0.5871 1 1 1 1

0.4629 1 1 1 1 1

Overall_Performances ACTUAL 0.49438

STANDARD 0.50562 GRADE COPPER

Table C.6 : (Modified)Fuzzy AHP Performance Calculation ( Site-1 Data)


107

APPENDIX D : Fuzzy Set Theory & Fuzzy Logic Concepts D.1 Fuzzy Set Members of a Crisp set takes the value either 0 or 1. But members of a fuzzy set can take any

value between 0 and 1, means it can take partial memberships. Thus a fuzzy set A in the uni-verse of discourse U may be represented as a set of ordered pairs of element “u” and its

membership grade” )(A

uµ ”, and it can be written as

}/))(,{(AA

Uuuu ∈= µ .

When U is continuous, a fuzzy set A can be written as

�=U A

uuA /)(µ

When U is discrete, a fuzzy set A is represented as

�=

=n

iii uuA

1A

/)(µ

D.2 Membership Function Every Fuzzy Set has linguistic classes. Each linguistic class has its own definition about how & when each element in the universe of discourse can become the member of that linguistic class. This definition about belonging is called “membership function” of that class. Figure 5.4 gives different membership functions and its graphical representation. D.3 Fuzzy Operations: Union & Intersection

If QandP be two fuzzy sets in U with membership functionsµµ QP and

respectively

then union, intersection of them can be written as QP∪µfor the union QP � and BA∩µ for

QP � and can be written as

)}(),(max{ uuQPQP

µµµ =∪ for all u∈U

)}(),(min{ uu

QPQPµµµ =

∩ for all u∈U

D.3 Fuzzy Rules

Fuzzy rule contains antecedents (the inputs) and consequents (the output). Antecedents may contain a single fuzzy set or may contain union or intersection of many fuzzy sets and Conse-quents normally refer to single fuzzy set for every rule. An example of fuzzy rule is

If '''''' zisRthenyisQandxisP Where x, y and z are the linguistic classes represented either by words or by numbers.


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A typical example of fuzzy rule is

In most of the cases we may have to deal with group of input fuzzy rules, which leads to many output combinations, but as a total we are interested in the single output. In such cases Sup-Star compositions like Min[max()] or Max[min()], helps to integrate all of them. In the current research Max[min()] composition is used, which means that the from the Antecedents groups, minimum value will be considered for every rule and from these outputs maximum values will be considered for final aggregation. In short we can say that UNION[ INTER-SECTION() ]. The output value of every rule will also have attached “linguistic class”and hence the reasoning stands valid irrespective of the value. D.4. Fuzzy Inference Fuzzy inference refers to the internal mechanism for producing output values for a given value through fuzzy rules. In short the inference process involves 3 steps: fuzzification, rule evaluation and defuzzification. Fuzzification process converts the input real world values or standardized values into grades of memberships and corresponding linguistic classes. These fuzzified grades/classes are evaluated through fuzzy rules for output grades/classes. Finally these output grades are again converted back to real world crisp output values through cen-troid calculation in defuzzification process. There are 2 known inference methods: Mam-dani’s approach and Sugeno approach. Mamdani approach considers complete fuzzy set for centroid calculation in defuzzification, but Sugeno approach take the Singletons as the high-est membership value and corresponding x-point of output aggregated fuzzy set and finds the weighted average of these singletons as defuzzified output value. D.4.1 Rule Implication & Aggregation Process The implication process evaluates individual rule over fuzzified grades and generates an out-put grade and output class. Now the Aggregation does 2 things. First it truncates the Conse-quent Fuzzy Set according to the grade obtained and secondly it does the Union of all these fuzzy sets.

If temperature is ‘hot’ then fan-speed is ‘high’ If stake_holders_agreement is ‘Very Good’ then Security_to_forested_land is ‘Excellent’


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D.4.2 Defuzzification Defuzzification process calculates the output crisp value from the aggregated resultant fuzzy set derived after rule evaluation. There are different ways of calculating output value, but widely used methods are: Center of gravity method and Height method. In the centroid method all the elements within the aggregated fuzzy sets are considered with its respective memberships and it Height method only Mean of Maximum membership value and its corre-sponding x-element is considered. Example: Let us consider Indicator P1.6. Suppose we have standardized values 0.8 for its verifier “Type of NTFP” and 0.4 for the verifier “Potential extraction of NTFP”. The fuzzified values val-ues of verifier 1 (V1) is 0.5 “Very High” and 0.2434 “Moderate”. For verifier 2 (V2), the fuzzified value is only 0.75 “Moderate”. Now there are two possible combination occurs one is V1 can be Very High and V2 can be Moderate, Second possibility is V1 can be Moderate and V2 can be Moderate. Hence respectively 2 rules are needed. In this case RULE 2 and RULE 5 are activated. The results of the RULE 2 is Good with the grade Min(0.5,0.75)=0.5. The result of the RULE 5 is Fair with the grade Min(0.2434,0.75) = 0.2434. Now the aggre-gation process truncates the Good fuzzy set with the grade 0.5 and Fair fuzzy set with 0.2434. These two sets are aggregated with Union function it finds and integrates the maximum val-ues available out of both the set (Figure D.2). Then finally output crisp value is calculated.

Antecedents ConsequentAntecedents Consequent

Figure D.1 : Fuzzy Mamdani Inference over Indicator P1.6

(Sustainability use & availability of NTFP)


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In a simple manner we can calculate the output as follows (0.32*0.2434) + (0.56*0.2434) + (0.63*0.5) + (0.87*0.5) approx. center of gravity = ----------------------------------------------------------------------- 0.2434 + 0.2434 + 0.5 + 0.5 = 0.9642 / 1.4868 = 0.6485 Since we have only used the approximated discrete points our result is not exact. If we use all the elements our correct result would be 0.66

In the Height method [(0.32+0.56)/2 ] * 0.2434 + [(0.63+0.87)/2] * 0.5 Output = ---------------------------------------------------------------------- 0.2434 + 0.5 0.44 * 0.2434 + 0.75*0.5 = -------------------------------------------------------- 0.7434 = 0.4821 / 0.7434 = 0.6485

Figure D.2 : Defuzzification Process


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APPENDIX E: Expert Rules used at different levels (Verifiers, Indicators, Criteria & Principle level)

The process of acquiring Expert rule is an important process in Fuzzy Logic Approach. Time & Care is needed from expert as well as analyst in this regard. Number of rules depend upon the number linguistic classes present for each input parameter. If the number of linguistic classes are 5 and number of input variables are 2 then 5*5=25 rules are needed. In general form number of rules needed can be written as Ln , where L is number of linguistic classes and n refers to number of input variables. All the verifiers are associated with 3 linguistic classes. Indicators, Criteria & Principle are associated with 5 linguistic classes. At Indicator level the number of rules for each indicator is related with number of verifiers involved. Except for Indicator P1.3 all other indicators un-der AM has 3 verifiers and each with 3 linguistic classes, hence number of rules are 33 = 27. For P1.3 there are 4 verifiers therefore number of rules become 3 4 =81. At Criteria level AM involves 4 indicators each with 5 linguistic classes and hence number of rules required for AM is 54 = 625. When Decision Maker provides the rules he has to be careful, though his consistency can be checked later. The Number of rules required at different hierarchy level of present LEI considered, without optimisation, is tablulated in the Figure E.1. Since the number of rules are huge and it would be difficult to understand if we present them in the tabular format. So we have to optimize them and we have to represent them efficiently. Decision Tree building process is generally used to efficiently and effectively represent the rules. In the current research I have used the software Xpert Rule Knowledge Builder (XRKB) developed by Attar Software Company (XRKB,2002). Explalining the process of making decision tree is beyond the scope of current research and hence is left to user to ex-plore. The optimized Decision Tree for representing rules at different levels are given in Figure E.2 to E.10.


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P 1.1

P 1.2

P 1.3

P 1.4

P 1.5

P 1.6

AreaManagement

ForestManagement

Sustainabilityof Forest

Resources

IndicatorsCriteriaPrinciple

1. Stake Holders Agreement

2. Legal Fulfillment

3. Boundary Demark & Impl.

1. Plan as per Land Capability

2. Plan as per Forest Types

3. Implementation

1. Forest Encroachment

2. Intensity of Forest Fire

3. Other Disturbances

4. Overcutting

1. Early Warning System

2. Skilled Labours

3. Community & Insti.Participation

1. Silviculture Implementation

2. Ecosystem Compliance

3. St. struc, Spec.comp., Tree Regen.

1. Types of NTFP

2. Potential Extraction

Verifiers

27 Rules

27 Rules

81 Rules

27 Rules

27 Rules

9 Rules

625 Rules

25 Rules

25 Rules

Figure E.1: Number of Rules required at Different Levels of LEI system (without optimisation)


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Figure E.2: Decision Tree used for Indicator P1.1



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115





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Figure E.8: Decision Tree used for the criteria Area Management (AM)


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Figure E.9: Decision Tree used for the criteria Forest Management (FM)

Figure E.10: Decision Tree used for the criteria Forest Resources Sustainability (FRS)


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APPENDIX F: Basic Terminologies and concepts of Type-2 Fuzzy Set

F.1 Type-1 Fuzzy Set and Type-1 Membership Function If the membership values of elements of a set cannot be described by a crisp values (0 or 1) and if the elements takes partial membership values then the set becomes fuzzy set. If the par-tial membership values are considered to be the exact (assumed to be real) representation then it is called type-1 fuzzy set. If the membership function used in such set is exact then it is called Type-1 membership function. If A is a fuzzy set then it can be represented as

If X is continuous then A can be written as

F.2 Type-2 Fuzzy Set (T2FS) and Type-2 Membership Function(T2MF) For many of the environmental applications the membership function chosen are subjective. In such cases the possible variations over the chosen membership function may be considered as uncertainty. If we include such varying membership function then it is called Type-2 membership function. The fuzzy set which makes use of T2MF is called Type-2 fuzzy set. Type-1 fuzzy set A will be written as Ã to represent type-2 fuzzy set.

Hence T2MF can be depicted using 3 axes: one for x values, one for membership function (u) and one for amplitude (weight of membership value to represent the uncertainty weight) [µ(x,u)]. Figure F.1 depicts the T2MF, where Cyan color represent the upper and Green color represents the lower part of Foot Print of Uncertainty (FOU) and Red color represent the type-1 principal membership curve without uncertainty.

A = { x,µA(x) | x ∈ X} Eq.(F.1)

A = � x∈X µA(x) / x Eq.(F.1.a)

�� = �x∈X �u∈Jx µ�(x,u)/(x,u) Jx ⊆ [0,1] Eq.(F.2)


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F.2.1. Primary Memberships In T2MF, the plane made by axes x and u makes the primary memberships. It refers to all the values of u where amplitude is greater than 0 for all the x. Primary membership at x is repre-sented by Jx. The primary membership values will be comparable to T1MF values if there is no uncertainty. Primary memberships have associated secondary memberships. We have to be clear here that Primary memberships are different from Primary membership function. Primary Membership Function refers to family of T1MF and is represented as µA(x). Primary membership functions can have bounded region of uncertainty and may be considered as footprint of uncertainty associated with it. We will see this later. F.2.2 Secondary Membership Function (SMF) When we include uncertainty in the Type-1 membership function then the resultant T2MF can be imagined as a 3-D membership solid curve/line (Figure F.1). If we consider only the “Variations of u and amplitude for a given x” then it will look like a Vertical Slice (plane made by the axes u and µÃ(x,u)) of total type-2 fuzzy membership function. This vertical slice is called Secondary Membership function of T2MF. The SMF can be written as

Figure F.1 : Gaussian Interval Type-2 Fuzzy Membership Function

with Upper and Lower FOU


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Using Eq.(F.3) in Eq.(F.2) will give us

If X and Jx are Discrete then the Eq.(F.4) will become

And can be expanded into

F.2.3 Secondary Grades In order to represent the uncertainty associated with each combination of (x,u), a weight can be associated with each pair of (x,u). The weight (Amplitude) of each membership values (u) for a given x is called secondary grades. If the weight value is more, then importance is more, which means that the uncertainty associated is less. Weight value range is between 0 and 1 (inclusive). fx(u) represents secondary grades at x. F.2.4. Interval type-2 membership function (I-T2MF) If the weight(amplitude) is uniform for all the u for all x then the type-2 fuzzy membership function becomes “Interval type-2 membership function”. In other words for a given Interval type-2 membership function the uncertainty associated with all the x and u are same or uni-form (i.e, constant). In such cases representation of T2MF just depends on the left and right end points. I-T2MF can be represented by its domain interval, which is represented by do-main centre and domain spread. Domain centre can be calculated as the mid point between left (l) and right (r ) end points as ( l + r) / 2. Domain spread from the centre can be calcu-lated as the half the difference between l and r, as ( l – r ) / 2 .

µ�(x=x’,u) = µ�(x’) = �u∈Jx f��(u)/(u) Jx ⊆ [0,1] Eq.(F.3)

� = �x∈X [ �u∈Jx f�(u)/(u)] / x Jx ⊆ [0,1] Eq.(F.4)

� = Σ i=1 to M [ Σk=1toN f��(u)/(u)] / xi Jx ⊆ [0,1] Eq.(F.5)

� = [Σk=1toN f��(u)/(u)] / x1 + [Σk=1toN f��(u)/(u)] / x2 + ...........

.......... + [Σk=1toN f��(u)/(u)] / xM Eq.(F.6)


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F.2.5. Triangular or Gaussian secondary membership function (T or G-SMF) If we use the amplitude variation similar to Gaussian function or Triangular function, which means that the mid point of secondary membership function plays important role and repre-sents the decreasing importance for the points away from the mid point, then such function can be called “Triangular-Secondary Membership function (T-SMF)” or Gaussian-Secondary Membership Function (G-SMF). F.2.6. Principal Membership Function In the 3-dimensional aspect, Union of all the points of u where secondary grade is 1 for every x is considered as Principal Membership function. If there is only one value having secondary grade 1 for each primary membership and it is located in the middle, then the principal mem-bership function will be similar to the type-1 membership function.

F.2.7 Foot Print of Uncertainty (FOU) Uncertainty in the primary memberships of a type-2 fuzzy set, consists of bounded region which is called Foot Print of Uncertainty. FOU is the union of all the primary memberships

F.3 Uncertainties in Gaussian Primary MFs Let us consider interval type-2 fuzzy membership function having Gaussian function of un-certainties over primary memberships. In this case there is a possibility of including uncer-tainty in three ways: 1) uncertain mean 2) uncertain standard deviation and 3) Proportional Variation of uncertainty with the variation of membership value (in the last one, it is assumed that lower membership values have less uncertainty and higher membership values have higher uncertainties). If we consider uncertaintity involved with mean then we get the FOU for Gaussian primary membership function as in Figure F.2. If we consider uncertaintity over standard deviation then we get the FOU for Gaussian primary membership function as in Figure F.3. In both the case FOU is bounded by two curves: one on top and one on bottom. These bounding curves can be considered as Upper membership function and Lower membership function respec-tively.

µprincipal(x) = �u∈X ( u / x ) where fx(u) = 1 Eq.(F.7)

FOU(��∪x∈X Jx Eq.(F.8)

�


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Lower Membership function is represented as --µÃ(x) and Upper Membership function as µ--Ã(x).

a) When Mean is not certain and varies over [m1,m2] the Lower membership function can be represented by

b) When Standard Deviation is not certain and varies as [σ1,σ2], then upper membership function will have only one gaussian function using m and σ2, while lower membership func-tion will depend upon only one gaussian function using m and σ1.

When all the sources of uncertainty vanishes, upper and lower membership functions be-comes equal, which reduces T2MF to T1MF.

��µ�(x) � --FOU(�) Eq.(F.9) µ��(x) � FOU(�)-- Eq.(F.10)

Upper Membership Function: µ��(x) = G(m1,σ;x) when x<m1 = 1 when m1�x�m2 Eq.(F.11 a) = G(m2,σ;x) when x>m2 Lower Membership Function:

��µ�(x) = G(m2,σ;x) when x�(m1+ m2)/2 Eq.(F.11 b) = G(m1,σ;x) when x>(m1+ m2)/2 where the Gaussian function G(m,σ;x) = exp{-(1/2) [(x-m)/σ]2 }

Upper Membership Function: µ��(x) = G(m,σ2;x) when x�(m1+ m2)/2 Eq.(F.12 a) Lower Membership Function:

��µ�(x) = G(m,σ1;x) when x>(m1+ m2)/2 Eq.(F.12 b)


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Figure F.2: Gaussian Membership function - Uncertainty in Mean

Figure F.3: Gaussian Membership Function - Uncertainty in Standard Deviation


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F.4 Embedded Type-2 Sets For every x we have number of u and secondary grades (associated amplitudes) in the pri-mary membership. Hence if we take just any one u from every primary membership for all the x, then we get just one Type-2 fuzzy set. If there are more values of u and associated variations in secondary grades, then for every x then the total number of possible combination of Type-2 Fuzzy sets are equal to the multiplication of number of elements of each primary memberships for all x. Hence a single Type-2 Fuzzy set can be viewed as a collection of type-2 fuzzy sets, which is then called as embedded type-2 fuzzy set. F.5 Type-2 Fuzzy Singleton In type-1 fuzzy singleton, the membership value is 1 at only one x. Similarly in Type-2 fuzzy set when the secondary grade at value x’ has the value 1 corresponding to the primary mem-bership of 1 & 0 and all other secondary grades are 0 in remaining primary memberships and for all other x values has 0 value in primary and secondary memberships then it is said to be type-2 fuzzy singleton. It can be written as

F.6 Union, Intersection and Complement Operations on Type-2 fuzzy sets

Let us take two type-2 fuzzy sets Ã and Ñ. The union of these two fuzzy sets can be written as

µ�(x,u) = 1/1 at x=x’ = 1/0 when x # x’

� ∪ Ñ = µ� ∪ Ñ ( x,v) = � x∈X µ� ∪ Ñ (x)/x = � x∈X [ �v∈Jx h�(v)/v] / x Eq.(F.13)

Where the union of secondary memberships takes the form

µ� ∪ Ñ (x) = µÃ(x) � µÑ(x)

= � u∈Jx �w∈Jx [fx(u) � gx(w)]/(u ∨ w) Eq.(F.14)

where � represents the join(union) operator over secondary memberships � represent the t-norm minimum or product operator

∨ represents the t-conorm maximum operator


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Similarly in the case of Intersection, we can write

Importantly, If the combination of (u ∨ w) or (u ∧ w) occurs more than once then the largest membership grade will be kept in the process. For the complement opertion on type-2 fuzzy set, it takes the form

F.7 Type-2 Defuzzification Since in Type-1 we have just only one possible membership values for every x in the final set (rule evaluated and aggregated), defuzzification is not a big problem. But Type-2 fuzzy set has large number of embedded type-2 fuzzy sets and hence for every embedded type-2 fuzzy set we have to calculate centroid and it leads to computationally complexity. Karnik and Mendel (1998) have provided an extension to type-1 defuzzification method, called “type-reduction”, by which one can compute the “Generalised Centroid” and its spread for the type-2 fuzzy set.

� ∩ Ñ = µ� ∩ Ñ ( x,v) = µÃ(x) � µÑ(x)

= � x∈X µ� ∩ Ñ (x)/x Eq.(F.15)

And

µ� ∩ Ñ (x) = � u∈Jx �w∈Jx [fx(u) � gx(w)]/(u ∧ w) Eq.(F.16)

where � represents the intersection operator over secondary memberships � represent the t-norm minimum or product operator

∧ represents the t-norm m inimum or product operator

µcomp(�� u∈Jx fx(u)/(1-u) = ¬µ�(x) Eq.(F.17)


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APPENDIX G: Software used & Future continuation For the present research I have used Arcview (from ESRI Inc.,) for spatial layer handling. For analysing different test sites data over different models, I have used a powerful matrix analys-ing software called MATLAB (Version 6.5, Release 13 from Mathworks Inc.,). For making the Decision Tree I have used the software Xpert Rule Knowledge Builder (XRKB) devel-oped by Attar Software Company (XRKB,2002). I had to write many MATLAB programs for the different approaches analysed in this re-search. For building Fuzzy Reasoning Model, I have used Fuzzy Logic Tool Box. Though this tool box provides easy way of making models it does not give membership values and step by step interaction values. So I had to write functions for fuzzy logic analysis and also for simulation. For Type-2 Fuzzy Logic there is no module available, so complete interaction sub-routines were written to analyse and to display them in 3D. User can also see some of my functions in the Mathworks website (www.mathworks.com) in fuzzy section. All the programs have detailed explanation in its own header and they also have necessary comments in between the programme to explain every portion. I have documented the name of each & every file, how to run them and every step by step guideline to repeat different ap-proach used in this research. Documents and all necessary program files are available with my both the supervisors, so that interested users can follow and test my research methods and related outputs later. Since my programs uses existing libraries for analysing Fuzzy Reason-ing model, user has to have license for Fuzzy Logic Tool Box module (otherwise it will not run) and for other models just normal MATLAB will be enough.