an approach to multi-criteria environmental evaluation with multiple weight assignment

An Approach to Multi-criteria Environmental Evaluationwith Multiple Weight Assignment

Boris Agarski & Igor Budak & Borut Kosec &

Janko Hodolic

Received: 6 August 2010 /Accepted: 12 September 2011 /Published online: 22 September 2011# Springer Science+Business Media B.V. 2011

Abstract In the domain of environmental protection,multi-criteria evaluation is used in cases where multiplealternatives, on the bases of multiple parameters, need to beevaluated. Depending on the particular goal of investiga-tion, various approaches have been developed and applied.This various multi-criteria approaches differ in parameterweighting method, in data normalization method as well asin the method for assessment of alternatives. According tothe applied multi-criteria methodology, the result, i.e., therank of alternatives may differ to some extent. In thiscontext, parameter weighting bears special significance inmulti-criteria evaluation, while the choice of method iscrucial for final result. The specificity of parameterweighting process in environment protection is directlyrelated to pronounced interdisciplinary character of thisarea, as well as the large number of influential parameters.With this in mind, this paper presents an approach to multi-criteria evaluation which—through integration of threespecific methods for parameter weighting—allows moreflexible and multi-purpose application. Based on theestablished concept, a software application was developed.Besides automated parameter weighting, it also provides

graphical interpretation of results. The developed approachand software have been verified on the case study related toevaluation of environmental loadings at six locations in thecity of Novi Sad.

Keywords Multi-criteria evaluation . Parameter weighting .

Alternative assessment . Environmental loading

1 Introduction

The problem of comprehensive evaluation of environmentalissues—which in principle depends on a number of parame-ters—lies in the diverse nature of those parameters and theirdimensional variety. In other words, total environmentalimpact cannot be expressed by simply aggregating particularvalues of influential parameters, i.e., criteria. Besidesparameters which represent direct influence on environ-ment, in order to perform a more comprehensiveevaluation, one often includes economic, social, andtechnological parameters which have indirect influenceon environment [27]. This is why in this area focus isplaced on the development and application of multi-criteria methods for evaluation of environmental impacts.

In the area of environment protection, multi-criteriaevaluation can be employed whenever there are multiplealternatives that need to be assessed and compared—e.g.,environmental loading on different locations [1], environ-mental assessment of products in eco-design [9, 25] or ineco-labeling [5], municipal solid waste management andplanning [3, 12, 16, 23], and environmental evaluation ofprocesses in Environmental Impact Assessment (EIA) [34]or for Best Available Technologies (BAT) [24]. An exampleof multi-criteria evaluation of environmental loading at

B. Agarski : I. Budak (*) : J. HodolicDepartment of Mechanical Engineering,Faculty of Technical Sciences, University of Novi Sad,Trg Dositeja Obradovica 6,21000 Novi Sad, Serbiae-mail: [email protected]: www.ftn.uns.ac.rs

B. KosecDepartment for Materials and Metallurgy,Faculty of Natural Sciences and Engineering,Askerceva cesta 12,1000 Ljubljana, Slovenia

Environ Model Assess (2012) 17:255–266DOI 10.1007/s10666-011-9294-y

particular locations is presented in [1]. Here, a multi-criteria methodology was used to evaluate the need forremediation of polluted areas, taking into considerationvarious aspects, such as the sediment quality, economic,and social aspects. Multi-criteria evaluation in analysis oftechnological solutions is presented by Sudhakar andShrestha in [35]. They applied a multi-criteria approachfor alternative evaluation of a transport system, i.e., thetype of motor vehicle. Schollenberger et al. [31] presenteda multi-objective pinch analysis and the results of itsapplication on analysis of eco-design of a bicycle frame.In [39], a multi-criteria evidential reasoning approach wasapplied to aggregate various environmental factors, for thepurpose of EIA.

Multi-criteria evaluation methods differ in conceptualdetails, regarding parameter (criteria) weighting, datanormalization, and the assessment of alternatives (theway of combining the normalized parameter values andweights in the evaluation result). According to this, theresult of quantitative multi-criteria evaluation (i.e., therank of alternatives), obtained by different evaluationmethods, may differ to some extent [11]. Parameterweighting plays an important role in multi-criteria evalu-ation. The choice of method for weighting parametersgreatly influences the final result, i.e., the rank ofalternatives. Thus, depending on the primary goal ofresearch, a number of different approaches have beendeveloped and applied. One of the roughest methods ofweight assignment is the direct weighting technique. Withthis technique, weights are assigned through directassessment of the importance of one parameter overanother, without considering how much the parameteractually contributes to the total score of the alternatives[3]. The next widely applied technique is pairwisecomparison, for which several methods exist. Mostprominent among them are the Fuller triangle andAnalytical Hierarchical Process (AHP). The first one isbased on the forming of triangular matrices of parameterpairs within which parameter weighting is performed [14,37] (described in more detail, further on). Unlike theprevious method, the AHP method, developed by Saaty[29], allows parameters to be classified into hierarchicallevels and uses a finer scale to compare their significance.Examples of AHP application for parameter weighting arepresented in [4, 15, 21, 22, 32, 33]. According to thetradeoff weighting method, the decision maker comparestwo alternatives which only differ in two parameters whilethe others are kept at the same level [20]. Swing weighting[38] is based on a questionnaire according to which thedecision maker first assigns maximum number of points tothe parameter he/she considers most important and then

assigns less points to the remaining parameters. Thesimple multi-attribute rating technique assigns weights toparameters in two steps. Firstly, parameters are rankedaccording to significance, and then the parameter isderived from the point ratio between the weightedparameter and the parameter with the least significance[8]. The issue of weight assignments to environmentalindicators was also discussed by Filar et al. [10]. Theyemployed the entropy concept to assign suitable weightsto the environmental indicators to reflect their relativeimportance in the assessment process.

The reason for such a large number of methods forparameter weighting should be found in the pronouncedinterdisciplinarity of problems which are the subject ofresearch in environment protection, as well as theircomplexity regarding the large number and variety ofparameters and alternatives. Among most important defi-ciencies of parameter, weighting methods are the pro-nounced subjectivity of decision makers, i.e., thecomplexity and slowness of the process in cases with largenumber of parameters and/or alternatives. This is why therehave been a number of attempts recently to overcomedeficiencies of individual parameter weighting methods bycombining them in order to solve particular problems. Suchattempts can be found in [6, 28].

This paper proposes an approach to multi-criteriaenvironmental evaluation which encompasses functionsfor parameter weighting, normalization of input data,and evaluation of alternatives. First of all, the proposedapproach has wide application area due to integrationof three alternative methods for parameter weighting:Fuller triangle method, which allows quick but roughparameter weighting; AHP, which allows a moreprecise and hierarchical weighting; and the method ofreduction coefficients (RC), which, due to automatedweighting, i.e., calculation of parameter weights, issuitable for larger sets of parameters and/or alterna-tives. RC method is also more objective, i.e., it is lessbiased by decision maker, which is the basic drawbackof the other two methods.

Presented in this paper is a software solution which isbased on the proposed approach. Besides flexibility anduniversality, this solution is also capable of variousgraphical presentations (bar chart and spider chart) whichallow a better review of results. The proposed approach andsoftware solution were tested on a case study of multi-criteria evaluation of environmental loading at six locationsin the city of Novi Sad. Special focus was placed onanalysis of application of all three parameter weightingmethods, as well as the testing of the function forevaluation of alternatives.

256 B. Agarski et al.

2 Background of the Proposed Approach

2.1 Parameter Weighting

Considering the fact that parameter weighting is one ofessential problems in multi-criteria evaluation, theauthors propose an approach which integrates threemethods for parameter weighting to achieve flexibilityand universality:

– Fuller triangle (FT) method,– AHP, and– Method of reduction coefficients.

FT method allows fast parameter weighting, provid-ed that the parameter sets are relatively small. FTmethod belongs to the class of pairwise comparisonmethods. Each pair—made up of two parameters beingcompared—carries one point, where the point isawarded to the more significant parameter (which isthen encircled). If a decision is made that they are ofequal importance—the parameters get half point each(this pair is then enclosed in a rectangle). Once theevaluation is finished, the points awarded to parametersare summed up, and the sums represent their weights.The total number of pairs being compared is:

N ¼ n n� 1ð Þ2

; ð1Þ

where n is number of parameters. N should equal the sumof all parameter weights [14, 37].

AHP method is often used for solving variousmulti-parameter problems. It allows a more preciseparameter weighting using multi-level criteria. Whencreating a decision tree, decision maker is allowed tofirst define weights of the basic criteria used forevaluation, and then he/she can define the lower levelsub-criteria which precisely define the examined multi-criteria problem. Application of multi-hierarchicalcriteria is especially suitable in cases with multiplecriteria which can be grouped into several functionalclasses [13].

The two previous methods require significant contribu-tion from an expert (decision maker), which involves his/hers subjective influence on parameter weighting. This is afundamental drawback of the previous two methods.Another significant drawback is related to complexity andslowness in cases when there are larger sets of parameters(e.g., 20 and more).

With this in mind, the proposed approach also involvesthe RC method, which allows automated parameter weight-ing. Its advantage is most prominent in cases of large

number of parameters, while its reliability increases withlarger samples, i.e., number of alternatives. Once the goal,alternatives, and parameters have been adopted, perfor-mance matrix Y can be formed to represent input data forcalculation:

Y ¼ yij� �

i¼1;2;...;n; j¼1;2;...;m: ð2Þ

Columns in matrix Y represent parameter values(denoted with j), while the rows represent alternatives(denoted with i).

The potential problem with parameters which havedifferent environmental impacts (positive/negative) issolved by adding negative sign to parameters valueswhich have a positive impact. In other words, the jcolumns of matrix Y, whose environmental impact isobviously positive, are multiplied by −1. This results in amatrix A:

A ¼ aij� �

i¼1;2;...;n; j¼1;2;...;m; ð3Þ

which has the same dimensionality as Y. If there are nosuch parameters with positive environmental impacts,matrix A is identical to performance matrix Y.

Reduction coefficients which represent parameterweights can be described as a measure of influence of eachparameter. The important part of parameter weighting inthis method is the parameter ordinalization. This means thatthe parameter in the first column will have maximuminfluence (weight equaled to 1) while the rest of parametersweights will have smaller values. Reduction coefficients,i.e., parameter weights wj of the jth parameter arecalculated as:

wj ¼Yj�1

i¼1

1� rij��

; j ¼ 1; 2; . . . ; n: ð4Þ

Variables rij represent correlation coefficients, calculatedas:

rjl ¼Pn

i¼1aij � aj� �

ail � alð ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1aij � aj� �2 Pn

i¼1ail � alð Þ2

s ;

j ¼ 1; 2; . . . ;m� 1; l ¼ 2; . . . ;m;

ð5Þ

where:

aij ordered value of j parameter in ith alternativeāj value of j mean values vector componentn number of alternatives.

An Approach to Multi-criteria Environmental Evaluation 257

An example that illustrates a parameter weighting byRC method, which allows reduction of subjectiveinfluence, is given in Table 1. The shift in the positionof parameter 1 (within the performance matrix) fromposition 1 to position 7 shows a constant decrease of itsweight (bolded numbers).

Here, it should be noted that in the determination ofweights using one of the first two methods, the valuesof criteria by alternatives (performance matrix) do notdirectly influence the final weight values. In contrast,with RC method, parameter values directly impactweight values, which the previously described mathe-

Table 1 Parameter weightingby RC method Order of parameters 1 2 3 4 5 6 7

Weights 1 0.5513 0.2716 0.7225 0.0227 0.0194 0.0412

Order of parameters 2 1 3 4 5 6 7

Weights 1 0.5513 0.2716 0.7225 0.0227 0.0194 0.0412


Weights 1 0.9691 0.1545 0.7225 0.0227 0.0194 0.0412


Weights 1 0.8022 0.9057 0.1489 0.0227 0.0194 0.0412


Weights 1 0.9578 0.7947 0.0285 0.1133 0.0194 0.0412


Weights 1 0.7657 0.9141 0.1051 0.0065 0.0999 0.0412


Weights 1 0.5166 0.7241 0.3867 0.0187 0.0098 0.0743

Data t(performance matrix)

inpu

Graphicalinterpretation(histogram)

Rank ofalternatives ( )qi

Datanormalization

Assessment ofalternatives

Graphicalinterpretation

(spider diagram)

Analytic hierarchyprocess

Weightingmethod

selection

Reductioncoefficients (k)i

Parametersweights (w)i

Fuller’s triangle

Weighting

Normalizeddata (B )ij

Evaluation

Graphicalinterpretation(histogram)

Consistencycheck

Fig. 1 Algorithm of thedeveloped software solution(VK Software)


Fig. 2 The main dialog panel ofthe VK Software

Fig. 3 The panels for parameterweighting in VK Software—aFT, b AHP, c RC


matical model clearly illustrates. In that respect, thismethod is more sensitive to the quality of input data,while at the same time it uses them more directly.

2.2 Assessment of Alternatives

In the proposed approach, evaluation of alternatives isperformed by multiplying the normalized parameter values(matrix A, defined in Section 2.1) with the assigned

weights, using one of the three previously describedmethods:

qi ¼Xm

j¼1

bij wj; i ¼ 1; 2; :::; n; ð6Þ

where:

bij normalized parameterswj parameter weight

Fig. 4 The positions of measuring spots

Table 2 Measured parameter values by locations [7]

Parameter/location

Total quantityof air-sediment[mg/m2]

CO2

concentration[mg/m3]

COconcentration[mg/m3]

Daily level ofcommunalnoise [dB]

Pass-byfrequency forheavy vehicles [–]

Pass-byfrequency forlight vehicles [–]

Pass-byfrequency formotorcycle [–]

1—Salajka 94.3 879.35 0.29 73 39 652 3

2—Detelinara 96.7 851.31 1.07 70 28 305 2

3—Telep 135.8 815.29 0.00 65 6 251 2

4—Grbavica 457.6 981.34 6.60 69 18 424 2

5—Stari grad 290.0 1,519.50 0.72 70 20 456 3

6—Petrovaradin 96.8 943.72 3.16 68 16 315 3


m number of parametersn number alternatives.

Dimensionless values qi are directly proportional toenvironmental influence (e.g., impact, loading, etc.) of theith alternative for the selected parameters. In other words,higher values of q indicate higher environmental influenceand vice versa. Based on the obtained results (qi), thealternatives are ranked, allowing user to gain insight intothe environmental influence of each alternative.

Parameter normalization—related to the problem ofvarious parameter dimensions (cubic meters, kilograms,decibels, etc.), i.e., their order of magnitude (10−2, 103,105)—is performed by applying the discriminationprinciple. According to this principle, positive difference(aij−uj) is divided by the values of standard deviations sj:

bij ¼ aij � ujsj

; i ¼ 1; 2; :::; n; j ¼ 1; 2; :::;m; ð7Þ

where:

aij ordered value of j parameters in ith alternativeuj value of j components of artificial vectorsj standard deviation of ordered j parameter (or deviation

parameter):

sj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xn

i¼1

aij � aj� �2

s; j ¼ 1; 2; :::;m; ð8Þ

where:

aij ordered value of j parameter in ith alternative

āj value of j mean values vector componentn number of alternatives.

Comparison of vectors is performed by adding ahypothetical alternative, also termed as artificial vector U:

U ¼ uj� �

j¼1;2;...;m: ð9Þ

Elements uj represent the allowed values of parameters(for example, boundary values of pollutant emissions intothe living environment) which, in an ideally formedalternative, represent minimum environment pollution.The difference between the real vectors of particularalternatives Aj and the artificial vector U of “ideal” valuesindicates the difference between a particular parameter andits allowed value that cannot be negative:

aij � uj � 0; i ¼ 1; 2; . . . ; n; j ¼ 1; 2; . . . ;m: ð10Þ

If the data on allowed values are unavailable forparticular parameters, the use of minimal parameter valuesis recommended to form the vector U. More specifically,artificial vector element uj is determined as the minimum ofthe jth parameter’s values (aij) of all n alternatives:

uj ¼ mini

aij; i ¼ 1; 2; . . . ; n; j ¼ 1; 2; . . . ;m: ð11Þ

3 Software System for Multi-criteria EnvironmentalEvaluation with Multiple Weight Assignment

Bearing in mind the complexity of the multi-criteriaenvironmental evaluation, it is clear that the use of softwareprocessing can significantly add to efficiency of the processand reliability of results. In this respect, this paper presentsa software solution termed VK Software, based on the

1 1

2 3 4 5 6 7

4 5 6 73

4 5 6 7

5 6

6 7

1 1 1 1

2 2 2 2 2

3 3 3 3

7

4 4 4

5 5

6

7

Fig. 5 Parameter weighting according to FT method

Table 3 Parameter weights obtained by FT method

Parameter name Parameter weight

1—Total quantity of air-sediment 4.50

2—CO2 concentration 1.50

3—CO concentration 0.50

4—Daily level of communal noise 3.00

5—Pass-by frequency for heavy vehicles 5.00

6—Pass-by frequency for light vehicles 5.50

7—Pass-by frequency for motorcycle 1.00


approach described in previous section, whose algorithm isshown in Fig. 1, while the main dialog panel of the VKSoftware is shown in Fig. 2.

This software solution consists of two modules:

1. Parameter weighting module and2. Module for evaluation of alternatives.

The modules were developed based on the conceptpresented in the previous section. The first module enablesoptional weighting with three different methods—FT, AHP,and RC. The panels for parameter weighting for eachmethod are shown in Fig. 3.

The software includes graphical representation of theobtained results—bar charts for parameter weights andthe calculated rank of alternatives, and polar diagram(also known as the spider diagram) to representnormalized parameter values by alternatives (Fig. 2). Inrecent years, due to its favorable characteristics, the“spider diagram” has been increasingly used for datarepresentation in multi-criteria analyses [17, 23, 26, 34].The area enclosed by the polygons is directly proportionalto the level of environmental influence (e.g., loading,impact, etc.) for a particular alternative (each colorcorresponds to a particular alternative).

Evaluation ofenvironmental

motor vehiclesloading by

Location 4Grbavica

Location 3Telep

Location 5Stari Grad

Location 6Petrovaradin

Location 2Detelinara

Location 1Salajka

Level 3P sarameter

Level 4Novi Sad city

locations

Level 1Multicriterialanalysis goal

Parameter group AAir quality

Parameter group BLevel of

communal noise

Parameter group C

requencyVehicle pass-by

f

Level 2Groups of

parameters

Parameter 5Pass-by

frequency forheavy vehicles

Parameter 6Pass-by

frequency forlight vehicles

Parameter 7Pass-by

frequency formotorcycles

Parameter 3Concentration

of carbonmonoxide

Parameter 2Concentration

of carbondioxide

Parameter 1Total quantityof sediment

matter

Parameter 4Level

communalnoise

of

Fig. 6 AHP decision tree

Table 4 AHP comparisonmatrix for parameters andparameter groups

Parameter group A Parameter group B Parameter group C Weights

Parameter group A 1 3 1/2 0.33

Parameter group B 1/3 1 1/3 0.14

Parameter group C 2 3 1 0.53

Parameter 1 Parameter 2 Parameter 3 Weights

Parameter 1 1 5 5 0.70

Parameter 2 1/5 1 2 0.18

Parameter 3 1/5 1/2 1 0.12

Parameter 5 Parameter 6 Parameter 7 Weights

Parameter 5 1 1/2 7 0.37

Parameter 6 2 1 6 0.56

Parameter 7 1/7 1/6 1 0.07


4 Verification

Verification of the proposed approach was performed ona case study dealing with evaluation of environmentalloading at locations in the city of Novi Sad. Theselection of representative parameters is of specialimportance for credibility of multi-criteria evaluation.Furthermore, for the selected parameters it is necessaryto define monotonically increasing or decreasing impacton environment. The application of variable impactparameters is limited to those with small variations, i.e.,those which can be described by mean value. Hereby,filtration of outliers using median method is recommended,considering their negative effect on determination ofmean value.

Having previous on mind, in this case study, thefollowing parameters (criteria) were selected for theevaluation of environmental loading:

– Total quantity of sediment matter,– Carbon–dioxide concentration,– Carbon–monoxide concentration,– Level of communal noise,– Vehicle pass-by frequency of heavy (transport)

vehicles,– Vehicle pass-by frequency of light (passenger) vehicles,

and– Vehicle pass-by frequency of motorcycles.

Shown in Fig. 4 are the positions of measuring spotswhich were grouped into six locations. The measuredparameter values are given in Table 2. Figure 4 shows thepositions of measuring spots which were grouped into sixlocations. During verification, the three built-in methodsfor parameter weighting were used. Using VK software,the alternatives were evaluated based on the calculatedweights. These results were checked through comparisonwith the results obtained by the well-known Technique for

Order Preference by Similarity to Ideal Solution (TOPSIS)method.

4.1 Calculation of Parameter Weights

The procedure of parameter weighting according to FTmethod is shown in Fig. 5, while the calculated weights arepresented in Table 3. Parameters weighting according toAHP method was based on hierarchical approach, presentedby the decision tree in Fig. 6. The goal of multi-criteriaanalysis (evaluation of environmental loading by motorvehicles) is positioned on top of the hierarchy. On thesecond level of the hierarchy are parameter groups (criteria)and on the third level are parameters (sub-criteria), whilethe last hierarchical level holds the locations in the livingenvironment (alternatives). In AHP weight assignment,every comparison between two elements of the hierarchyis performed based on the Satty’s scale, while the results ofcomparison between elements are written into appropriatecomparison matrix (Table 4). Final parameter weights arederived by multiplying weights of parameter groups, fromthe first level, by parameter weights from the second levelof hierarchy (Table 5). Consistency was analyzed for the

Table 5 Calculation of parameter weights by AHP method

Parameters on the first hierarchy level Weights of parameters Parameters on the second hierarchy level Weights of parameters

A—Air quality 0.33 1—Total quantity of air-sediment 0.23



B—Level of communal noise 0.14 4—Level of communal noise 0.14

C—Vehicle pass-by frequency 0.53 5—Pass-by frequency of heavy vehicles 0.20

6—Pass-by frequency of light vehicles 0.29

7—Pass-by frequency of motorcycles 0.04

Sum of parameter weights 1.00 Sum of parameter weights 1.00

Table 6 Parameters weight obtained by RC method

Parameter name RC (parameter’s weight)

1—Total quantity of air-sediment 0.8822



4—Daily level of communal noise 0.0051

5—Pass-by frequency for heavy vehicles 0.1651

6—Pass-by frequency for light vehicles 1.0000

7—Pass-by frequency for motorcycle 0.0551


derived parameter weights on both levels of hierarchy, bycalculating the degree of consistency according to [29].Considering that all of the calculated consistency indicesare lower than 0.1, one can conclude the derived weightsare satisfactory.

According to the concept of RC method, parameterswere sorted into following sequence by their relativesignificance: 6, 1, 5, 4, 2, 7, 3. Reduction coefficients,i.e., parameter weights, are shown in Table 6.

4.2 Assessment of Alternatives

As mentioned at the start of this section, the ranks ofalternatives were calculated on the basis of all threeparameter weighting methodologies described in Sec-tion 2.2. In order to test the proposed approach, the sameproblem was solved using the TOPSIS method. TOPSISclaims that the chosen alternative should be at the shortestdistance from the “ideal solution,” while maintaining thelargest possible distance from the “anti-ideal” solution.This method is described in more detail in [2, 18]. Shownin Figs. 7 and 8 are comparative representations of results,normalized according to:

qNORMi ¼qi

P6

k¼1qk

; i ¼ 1; 2; . . . ; 6: ð12Þ

5 Discussion

Analysis of comparative results shown in Fig. 7 revealedthe following:

– Three groups of locations are identified: highly loadedlocations (1, 4, and 5), medium-loaded locations (2 and6), and least-loaded locations (3).

– The ranks of alternatives calculated on the basis ofparameter weights, obtained by FT and AHP methods,are almost identical (Fig. 7). This is logical, bearing inmind similar methodologies used by these two methods,which generated almost identical parameter weights(Fig. 9), normalized according to:

wNORMj ¼wj

P7

k¼1wk

; j ¼ 1; 2; :::; 7: ð13Þ

– Although similar to the previous two ranks, the rank ofalternatives which was calculated based on weightparameters generated by the RC method is somewhatdifferent. The difference is in the order of the mostloaded locations. As opposed to the previous two cases,which resulted in the 1–5–4 order, in this last case theorder was 4–5–1. This can be explained by highervalues of parameter weights 1 and 6 (Fig. 9), whichresults in their increased influence on alternatives 4 and

Fig. 7 Comparative reviewof results obtained by VKSoftware

Fig. 8 Comparative review ofresults obtained by TOPSIS


5 (Table 7). Bearing in mind the different loads in thesetwo alternatives, one concludes that the RC methodproved its applicability even with a smaller set ofparameters. However, it should be noted that—consid-ering the uncertainty of calculation of correlationcoefficients which decreases with the increase of thenumber of alternatives [14, 36]—the RC method ismore suitable for complex problems.

Based on the results shown in Figs. 7 and 8, it can beconcluded that the trend of alternative ranks obtained byVK Software corresponds to the one obtained by TOPSIS,which confirms its functionality and validity of theproposed methodology for evaluation of alternatives.

6 Conclusion

The method of multi-criteria evaluation has been in the focusof environment protection experts for a number of years now.The specific trait of multi-criteria evaluation in this area is apronounced interdisciplinarity which is especially importantin parameter weighting. Hence, in this paper, a method formulti-criteria evaluation is proposed which integrates threecharacteristic methods for parameter weighting, thus allowinga more flexible and multi-purpose application. Based on theproposed concept, a software solution named VK Softwarewas developed. This software allows automated evaluation, aswell as the graphical representation of results.

The developed approach and VK Software have beenverified on a case study by evaluating environmental

loading at six locations in the city of Novi Sad. Consideringthe results presented in this paper, the authors conclude thatthe developed approach and the software solution per-formed satisfactorily, regarding functionality and practicalapplicability.

The authors should especially like to emphasize appli-cability of the developed system in cases with large numberof criteria and alternatives, which is due to the integratedRC method. This is very important, bearing in mind thegrowing complexity of parameters in the emerging real-world environmental issues.

Considering uncertainty in the area of multi-criteriadecision making, and bearing in mind the results of recentinvestigations pertaining to control of uncertainty inpairwise comparisons [19, 30] (characteristic for all threeweighting methods), future investigations shall be directedtowards implementation of fuzzy logic in parameterweighting.

In addition, one of the future steps for improvement ofthe developed approach should be the implementation offilter for statistical outliers in input data. Besides thealready mentioned preparation of input parameters whoseenvironmental impact oscillates around some mean value,the filter should allow preparation of data in case of a largernumber of measuring spots with certain alternatives.

Finally, although the proposed method presented in thispaper was verified on environmental loading problem, itcan also be applied in other areas such as BAT selection,EIA, eco-design, or other areas related to environmentalmulti-criteria decision-making problems. According to this,future investigations shall include application of thedeveloped approach in the mentioned environmental fields.

Fig. 9 Comparative review ofobtained parameter weights

Table 7 Normalized parametervalues (matrix B) Parameter/Location 1 2 3 4 5 6 7

1—Salajka 0.00 0.27 0.13 3.32 3.21 3.02 2.00

2—Detelinara 0.02 0.15 0.46 2.08 2.14 0.41 0.00

3—Telep 0.31 0.00 0.00 0.00 0.00 0.00 0.00

4—Grbavica 2.67 0.69 2.86 1.66 1.17 1.30 0.00

5—Stari Grad 1.44 2.94 0.31 2.08 1.36 1.54 2.00

6—Petrovaradin 0.02 0.54 1.37 1.25 0.97 0.48 2.00


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http://dx.doi.org/10.1186/1750-0680-4-4

an approach to multi-criteria environmental evaluation with multiple weight assignment

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