fuzzyprincipalcomponentanalysismodelonevaluating...

Research ArticleFuzzy Principal Component Analysis Model on EvaluatingInnovation Service Capability

Hui Wu and Xiao-min Gu

School of Financial Technology Shanghai Lixin University of Accounting and Finance 995 Shangchuan Road Pudong New AreaShanghai 201209 China

Correspondence should be addressed to Xiao-min Gu guxiaominlixineducn

Received 9 June 2020 Revised 23 June 2020 Accepted 26 July 2020 Published 30 September 2020

Academic Editor Lu Zhen

Copyright copy 2020 Hui Wu and Xiao-min Gu+is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

+is article mainly evaluates the regional innovation service capacity through the TOPSIS method Firstly a regional collaborativeinnovation network is constructed and the Yangtze River Delta region is selected for analysis Secondly an evaluation index isconstructed for innovation service capability fuzzy principal component analysis is used to refine quantitative and qualitativeindex data of innovation service capability and the index weight is calculated +en the region of the Yangtze River Delta isselected and TOPSIS method is used to assist in the effective decision-making process of the evaluation of innovative servicecapabilities Due to the large amount of data in this article MATLAB programming is used Finally through the comparativeanalysis of the results countermeasures and suggestions are put forward from the perspective of the improvement of collaborativeinnovation service capabilities

1 Introduction

+e development of regional collaborative innovation isconducive to promoting the rapid development of the re-gional economy optimizing the efficiency of innovationresource allocation transforming factor-driven to innova-tion-driven and promoting the overall improvement ofregional economic competitiveness +e collaborative in-novation model with scientific structure and active com-munication is conducive to the establishment of a long-termand effective scientific and technological cooperationmechanism between regions However due to the imbalanceof resource allocation disparity in development levelssimple repeated construction and disorderly vicious com-petition among regions the development of regional col-laborative innovation has seriously hindered the promotionof regional collaborative innovation

Collaborative innovation theory is the theoretical basisof cross-regional collaborative innovation After Hakenproposed synergetics in 1976 different scholars elaboratedcollaborative innovation from different angles Kim [1]

analysed the ways in which companies enhance internationalcompetitiveness by synergizing internal and external in-formation and other innovative elements Huber [2] believesthat innovation promotes the spiral of organizationallearning through process practice so that the innovationability in collaborative innovation is endogenous in theinnovation elements Radosevic [3] conducted research onthe synergy between technological innovation and institu-tional change and believed that the key to determining thesuccess of corporate innovation lies in the coordinateddevelopment of technology and many nontechnical ele-ments Power [4] believes that innovative ideas processesgroups and organizations are important elements of col-laborative innovation Morris [5] empirically studied theimportant impact of innovation factors on high-tech RampDthrough social networks and further enriched the means forachieving collaborative innovation

In the current research trends of regional collaborativeinnovation foreign scholarsrsquo research on cross-regionalcollaborative innovation focuses on the research perspectivethe relationship with innovation performance and

HindawiScientific ProgrammingVolume 2020 Article ID 8834901 9 pageshttpsdoiorg10115520208834901

influencing factors In terms of research perspectives theperspectives of papers and patents strategic emergingindustries and industrial ecosystems are introduced [6]+e research on the relationship between regional col-laborative innovation and innovation performance focuseson the evaluation of cross-regional system innovationcapability [7] +e research on the influencing factors ofregional collaborative innovation is carried out from theperspective of collaborative cooperation tendency inno-vation driving factors and the cooperation relationship ofinnovation subjects [8 9] +e domestic scholarsrsquo researchon cross-regional collaborative innovation ability mainlyfocuses on the evaluation of innovation ability the researchon the influencing factors and mechanism and mode ofinnovation ability +e evaluation of cross-regional col-laborative innovation capability provides different insightsfrom different perspectives covering research methodssuch as dynamic evaluation methods comparative analysismethods DEA and Malmquist index [10 11] +e researchon the influencing factors of cross-regional collaborativeinnovation capability has analysed its influencing factorsfrom different research perspectives including policyconditions network development resource investmentexternal learning and communication Some scholars havealso explored the mechanism and model of cross-regionalcollaborative innovation starting from the perspective ofsynergetic undertaking industrial transfer and technologydiffusion

Innovative service capability refers to the comprehensiveevaluation of the effect of a service innovation activity by anenterprise +e innovative service capability not only reflectsthe effectiveness of the organizationrsquos operations and marketcompetition but also reflects the projected development leveland actual effect of the organizationrsquos projects In recentyears research on innovative service capabilities has mostlyfocused on service-oriented enterprises and manufacturingindustries that provide products and services at the sametime [12 13] In order to achieve effective market compe-tition not only service-oriented enterprises andmanufacturing-oriented enterprises but also high-tech en-terprises also strive to provide customers with perfect ser-vices and constantly carry out service innovation activities inorder to improve the service quality of enterprises therebyattracting and retaining customers and stabilize or expandthe market [14 15] In addition under the leadership ofregional collaborative innovation whether an enterprisersquosinnovation service capability can be improved is crucial tothe overall performance of the enterprise

It can be seen by combing the relevant research at homeand abroad that the existing literature provides a basicanalysis framework for the expansion of innovation servicecapabilities and sustainable development at the practicallevel but there are relatively few studies on regional in-novation service capabilities and the existing evaluationindicators +e synergy between innovation elements in thesystem has not been considered One of the purposes of themeasurement and evaluation of innovation service capacityis to form a more effective governance mechanism andmodel to promote the development of interregional system

innovation so it is necessary to study the evaluation ofinnovation service capacity

Based on the current status of regional collaborativeinnovation development this study is dedicated to buildingan evaluationmodel for innovation service capabilities Firstthis study uses fuzzy principal component analysis to refinequantitative and qualitative indicator data for innovationservice capability selection and calculates index weightsSecond this study uses TOPSIS to assist in the evaluation ofinnovative service capabilities Due to the large amount ofdata in this article this study was implemented usingMATLAB programming Finally through a comparativeanalysis of the results this article obtained an optimizationplan for improving innovation service capabilities andproposed countermeasures and suggestions on how to guidethe flow of innovation elements and improve regionalcollaborative innovation

2 Evaluation Index System Construction andEvaluation Method

21 Regional Collaborative Innovation Network Citing theARA business network model proposed by Hakansson andSnehota [16] (Figure 1 combined with the relationshipbetween actors and social networks involved in social net-work analysis a regional collaborative innovation network isdefined +e commercial network contains three elementsparticipants resources and activities It can be seen that ifyou want to research a network you must first define thenetwork and secondly define the participants (or actors)resources and activities (social relations) +e resources andactivities here can be collectively referred to as relationshipsand they have an inseparable relationship with the partic-ipants In addition there are relationships among partici-pants resources and activities In order to facilitatemeasurement they are called relationships here As a resultthe participants and relationships of a network are definedand the boundaries of the network are clearly defined

Participants in collaborative innovation networks usu-ally cover enterprises universities scientific research insti-tutions intermediary services governments etc but thecore network of cooperative innovation networks mainlyincludes enterprises universities and scientific researchinstitutions networks composed of governments interme-diary services etc are marginal network which can also becalled a related network +e main research of this study isthe core network that is the main body of the network isenterprises universities and scientific research institutions

+e regional collaborative innovation network studied inthis paper selects the biopharmaceutical industry in thehigh-tech industry and builds a collaboration based on therelationship between companies universities and scientificresearch institutions in the biopharmaceutical industry andthe application of patent (national invention patents andutility models) innovation network +e results of the visualanalysis of the development of the biological medicine in-dustry in the Yangtze River Delta are shown in Figure 2

It can be seen from Figure 2 that the innovation ability ofuniversities in the collaborative innovation network of the

2 Scientific Programming

biomedical industry in the Yangtze River Delta is obvious Itcan be seen from the figure that the more prominent nodesare Fudan University East China University of Science andTechnology and Shanghai Jiaotong University which showsthat the role of universities in regional collaborative inno-vation is far greater than that of enterprises and scientificresearch institutions Moreover the collaborative innova-tion cooperation between enterprises and scientific researchinstitutions also relies on colleges and universities andcolleges and universities have outstanding effects in regionalsystem innovation

22 Construction of Evaluation Index System for InnovationService Capability +is article takes the ldquoChina RegionalInnovation Capacity Reportrdquo undertaken by the ChinaScience and Technology Development Strategy ResearchGroup as an example to describe the overview of the in-novation capacity evaluation index system First of all theinnovation subjects of the regional innovation capability

framework are universities RampD institutions enterprisesintermediary institutions and governments Secondly theframework takes into account the flow of innovation ele-ments among innovation entities and the innovation ca-pability of the innovation entities themselves +irdly theframework emphasizes the importance of the constructionof an innovation environment and points out that thegovernment needs to carry out function transformation topromote technological innovation of enterprises Finally theinnovation capability framework takes into account thethree dimensions of regional development stock relativelevel and growth rate On the basis of the above analysisframework we constructed five first-level indicators 20second-level indicators 40 third-level indicators and 137fourth-level indicators including knowledge creationknowledge acquisition enterprise innovation innovationenvironment and innovation performance Regional in-novation capability index system

On this basis combined with the needs of innovationservice capability assessment the five indicators of knowl-edge creation knowledge acquisition enterprise innovationinnovation environment and innovation performance areassisted in three aspects regional collaborative innovationinput regional collaborative innovation output and regionalcollaborative innovation conditions Construction of indi-cators specifically when establishing an evaluation indicatorsystem selects indicators from four aspects simplicityrelativity representativeness comparability and feasibilityof indicators [12 13 15 17] +e specific evaluation indexsystem for innovation service capability is shown in Table 1

23 EvaluationMethod of Innovation Service Capability in theYangtze River Delta

231 Selection of TOPSIS Method Simply simplifying thedata and reducing the dimensions cannot tell whether thedecision is effective +e problem of innovation servicecapability evaluation belongs to the category of multi-objective decision-making so the problem can only besolved effectively by using good decision-making methodsTOPSIS (Technology for Order Preference by Similarity toan Ideal Solution) method is an analysis method for solvingmultiobjective decision-making problems with limited

Actor

ActivitiesResources

1 Participants control resources individually or

jointly

2 Participants have a certain understanding of

resources

1 Participants carry out activities

2 Participants have a certain understanding of the activity

1 The activity makes the resources interconnected

2 Through the use of other resources sensation can exchange resources

Business network

Figure 1 ARA business network model [16]

Figure 2 Visual analysis of the regional coordinated innovationnetwork of the biomedical industry in the Yangtze River Delta

Scientific Programming 3

solutions [18] Its logical relationship is relatively simple andclear with good interactivity and easy implementation Atpresent this method has been applied to the research of in-novation service capability evaluation+erefore the reason forchoosing the TOPSIS algorithm in this study is as follows

(1) +e indicators in this article are more objective andit is not suitable to choose subjective evaluationmethods such as intuitive judgment method andlinear weighting method

(2) +e evaluation results in this paper do not involvecost and efficiency so the activity cost method anddata envelope algorithm are not used

(3) +e indicator data in this paper are relatively smallso if the artificial neural network algorithm is notused the results will not converge

(4) +e indicators in this article are clear and there is nogreater ambiguity so fuzzy comprehensive evaluationmethod and gray system theory method are not used

3 Model Principle

31 Principle of Fuzzy Principal Component AnalysisPrincipal component analysis is a statistical analysis methodthat converts multiple variables into a few principal com-ponents through dimensionality reduction techniqueswhich uses the original more evaluation indicators withsimplified comprehensive principal component indicatorsInstead the comprehensive indicator retains most of theinformation of the original variables and is not related toeach other which can simplify complex problems +e fuzzyprincipal component analysis method is based on the var-iance contribution rate of the principal component com-bined with the fuzzy theory to obtain a reasonable correctionweight +e specific process is as follows

After standardizing the secondary indicators of theoriginal data perform weighted synthesis to obtain theevaluation value of the primary indicators

ηij aij

1113944n

i1 aij1113872 11138732

1113969 where i 1 2 n

j 1 2 k

(1)

In the formula aij represents the evaluation value ofthe j-th secondary index of the i-th region and ηij

represents the evaluation value of the i-th secondaryindex of the j-th region after normalization +ecomprehensive weighting of the secondary indicatorsyields xlowastij wijηij where wij is the weight of thesecondary indicators in the correspondingindicatorsPrincipal component analysis of first-level indicatorsInitial sample matrix Xlowast (xij

lowast )ntimesp wherei 1 2 n j 1 2 p

(1) Standardize the index according to the xij xlowastij minus

xlowastj slowastj formula to obtain a standardized evaluationmatrix X (xij)ntimesp In the formula xlowastj and slowastj arethe sample mean and sample standard deviation ofthe j index respectively

(2) Calculate the correlation coefficient matrix Rptimespeigenvalue λ1 ge middot middot middot ge λp ge 0 and normalized ei-genvector Eij between indicators

(3) Using the unit feature vector corresponding to theprevious eigenvalue of p the principal componentof p can be expressed as a linear combination of theoriginal indicators thereby obtaining the principalcomponent equation

Table 1 Innovation service capability index system

First-level indicators Secondaryindicators +ird-level indicators Unit Code Citations

Regional collaborative innovationinvestment

Enterprise Number of enterprises Pc X1 [12]RampD personnel People X2 [13]

Efficient Number of universities Pc X3 [15]RampD personnel People X4 [17]

RampD institutionsNumber of RampD institutions Pc X5

RampD personnel People X6Government finance technology grant Billion X7

Government

Government financial project appropriation Billion X8Government science and technology project

implementation funds Billion X9

Scientific papers Article X10

Regional collaborative innovationoutput Results

Patent application Item X11Patent ownership transfer Item X12

Form an expert or industry standard Item X13New product sales revenue Billion X14Patent transfer income Billion X15

Assistance in regional collaborativeinnovation

Economic basisGDP Billion X16

Financial institution loan balance Billion X17Employed population People X18

Resident life Number of college graduates or above People X19


Fij XijEij i 1 2 n j 1 2 p (2)

(4) +e variance contribution rate of the j principalcomponent is μj λj1113936

p

j1 λj When the cumulativevariance contribution rate μ 1113936

mj1 μj reaches a

certain value (generally not less than 85) the firstm

principal components Fi1 Fi2 Fim(i 1 2

n) are taken that is the m principal componentsare considered to reflect the information of theoriginal p evaluation indicators with fewerindicators

(5) Use the variance contribution rate of each principalcomponent as the initial weight and modify theinitial weight to obtain the final weight +e reason isthat when evaluating the original indicators eachexpert gives the number of weight intervals of eachindicator and the optimism of the collaborative in-novation ability of each candidate area according tothe needs of the enterprise For this purpose it isnecessary to calculate the weight Wi wij1113966 1113967i 1 2 n j 1 2 m that corrects theweight of the principal component and correct theweight of the principal component +e specificcorrection process is as follows

B pj qj1113960 11139611113872 1113873 1 minus aj1113872 1113873pj minus pmin

pmax minus pmin+ aj

qj minus qmin

qmax minus qmin

(3)

+e weight fuzzy set B [p1 q1] [p2 q2] [pn qn]1113864 1113865 isthe value of the weight interval of the evaluation indexand B([pn qn]) indicates the relative importance of theindex In the formula pmin min1ltjltnpj pmax

max1ltjltnpj qmin min1ltjltnqj qmax max1ltjltnqj andaj represents the optimistic coefficient for the region0lt aj lt 1+erefore normalizing the important membershipdegree can get the index weight as follows

wij B pj qj1113960 11139611113872 1113873

1113944m

j1B pj qj1113960 11139611113872 1113873 i 1 2 n (4)

(6) Amend the preliminary weight to obtain the finalweight of the regional innovation capability evalu-ation index

βi wijμj

1113944m

j1wijμj

i 1 2 n (5)

32 Principle of TOPSIS Evaluation Method Similarity toideal solution sorting method TOPSIS is a commonly usedscheme limited multiobjective decision analysis methodwhich has the ideal solution and negative ideal solution tosort the program set by means of a multiproperty issue +eideal solution is a virtual best solution that does not exist inthe solution set and each of its attribute values is the best

value in the solution the negative ideal solution is the virtualworst solution and each attribute value is the best in thesolution Poor value All the alternatives in the solution setare compared with the distance between the ideal solutionand the negative ideal solution +e solution that is close tothe ideal solution and far from the negative ideal solution isthe best solution +e specific evaluation steps are as follows

321 Construct the Initial Matrix +ere are n candidateprograms and m evaluation indicators and xlowastij representsthe evaluation value of the j index of the i program and theinitial matrix V of the principal component obtained by V

XlowastT

U (U is the coefficient matrix) is standardized accordingto vij vlowastij

1113936

Ni1 (vlowastij )2

1113969 i 1 2 n j 1 2 m +e

standardized matrix A (aij)ntimesm is obtained

322 Construct Weighted Normalization Matrix

B ATW

w11a11 w12a12 w1ma1m


wn1an1 wn2an2 wnmanm

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (6)

Among them Wntimesm are the correction weights obtainedby fuzzy principal component analysis

323 Determine the Ideal Solution B+ and Negative IdealSolution Bminus

B+

maxi

bij | j isin J1113876 1113877 b+1 b

+2 b

+j b

+m1113960 1113961 i 1 2 n

Bminus

mini

bij | j isin J1113876 1113877 bminus1 b

minus2 b

minusj b

minusm1113960 1113961 i 1 2 n

(7)

324 Calculate the Distance +e distance between theevaluation value and the ideal solution and the negative idealsolution is given by

s+i

1113944

m

j1bij minus b

+j1113872 1113873

2

11139741113972

sminusi

1113944

m

j1bij minus b

minusj1113872 1113873

2

11139741113972

(8)

325 Determine the Relative Proximity Ci

Ci s

minusi

sminusi + s

+i

i 1 2 n 0leCi le 1 (9)

326 Sorting Preference +e schemes are sorted and se-lected in the order of Ci from large to small and the relativecloseness Ci selects the optimal scheme which is the areawith the highest innovation service capability


4 Case Study

In May 2010 the State Council formally approved theimplementation of ldquothe Regional Plan for the Yangtze RiverDelta Regionrdquo +e document states that the Yangtze RiverDelta includes Shanghai Jiangsu and Zhejiang In 2014 theldquoGuiding Opinions of the State Council on Relying on theGolden Waterway to Promote the Development of theYangtze River Economic Beltrdquo also made it clear for the firsttime to include Anhui Province in the Yangtze River Delta toparticipate in development In May 2016 the StandingCommittee of the State Council formally adopted theldquoDevelopment Plan for the Urban Agglomeration of theYangtze River Delta Regionrdquo +e plan clearly mentionedthat Shanghai should play a leading role to promote thecommon development of various metropolitan areas in-cluding Nanjing Metropolitan Area Hangzhou Metropoli-tan Area Hefei Metropolitan Area Suxi ChangzhouMetropolitan Area and Ningbo Metropolitan Area +eYangtze River Delta urban agglomeration is complete withlarge medium and small cities with one megacity onemegacity 13 large cities 9 medium cities and 42 small cities+e Yangtze River Delta is a typical region for regional

collaborative innovation development and this study usesthis as an object for case analysis

41 Expert Questionnaire Survey and Data CollectionTable 2 shows the original data and initial weights for en-terprises to evaluate suppliers and Table 3 shows the resultof weighted standardization of the secondary indicators oftheir original data +e expert survey method was used toverify the construction of innovative service capabilities inthis study and then the corresponding indicator data wereselected +e data involved in this article were all from theChina Statistical Yearbook the China Science and Tech-nology Yearbook and the statistical yearbooks of variousprovinces and cities

42 Fuzzy Principal Component Analysis According to theinitial evaluation weight interval of each index [17 23] [1118] [6 9] we use the fuzzy algorithm to obtain the modifiedweight Wi and the final principal component weights βjrespectively

a1 095 W1 (03339 0 04965 01696) β1 (05299 0 03836 00865)

a2 076 W2 (03361 0 04834 01805) β2 (05340 0 03739 00921)

a3 082 W3 (03354 0 04875 01771) β3 (05327 0 03770 00903)

a4 065 W4 (03373 0 04762 01865) β4 (05362 0 03686 00952)

(10)

Among them a1 a2 a3 and a4 are known expertrsquos op-timistic coefficients for innovation service capability

43 TOPSISEvaluation In order to adapt to the problem ofindex selection and evaluation of innovation service ca-pability with many indexes this article uses MATLABprogramming to implement the TOPSIS algorithm whichnot only saves time but also provides results more accu-rately +e specific calculation process and results are asfollows

431 Construct the Initial Matrix In this paper there are 4candidate programs namely 4 regions and 3 evaluationindicators xij represents the evaluation value of the j indexof the i program +e initial evaluation matrix V is obtainedby multiplying the initial matrix X by the coefficient matrixU

V

976278 763622 799790

401815 1128293 374480

94977 413866 482996

896354 372349 705447

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (11)

Normalize according to vij vlowastij 1113936

6i1 (vlowastij )2

1113969

j 1 2 4 and get a standardized matrix A (aij)4times3


B ATW

02873 00462 02367

01192 00354 01080

00281 00116 01405

02669 00416 02006

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (12)

Among them W

05299 00865 0383605340 00921 0373905327 00903 0377005362 00952 03686

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ are the

correction weights obtained by fuzzy principal componentanalysis

433 Determine the Ideal Solution Bminus and Negative IdealSolution Bminus From B+ [max

ibij|j isin J] [b+

1 b+2

b+3 ] i 1 2 4 get

B+

03356 02367 004621113858 1113859 (13)


From Bminus [mini

bij|j isin J] [bminus1 bminus

2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)

434 Calculate the Distance between the Evaluation Valueand the Ideal Solution and the Negative Ideal SolutionFrom s+

i 1113936

3j1 (vij minus v+

j )21113969

i 1 2 4 get the distancebetween the evaluation value and the ideal solution

s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936

3j1 (vij minus vminus

j )21113969

i 1 2 4 get thedistance between the evaluation value and the ideal solution

s+

03618 01535 01537 032201113858 1113859 (16)

435 Determine the Relative ProximityC From Ci sminus

i sminusi + s+

i i 1 2 4 0leCi le 1 get

C 08822 03785 08055 032171113858 1113859 (17)

+ink of the value of Ci as a score for the innovationservice capability of each region and select a better regionBecause of C1 gtC3 gtC2 gtC4 the first area Shanghai has ahigher innovation service capability than other areas

5 Conclusions and Recommendations

51 Research Conclusion +e innovation of this studymainly lies in the innovation of methods In the regionalcollaborative innovation network the evaluation of inno-vation service capability is very important At present themost commonly used methods are fuzzy clustering DEAmethod AHP method and fuzzy analytic hierarchy processWhen analyzing these methods it is not difficult to find thatthe current innovation service capacity evaluation involves

too many indicators +e calculation process becomes verycomplex even difficult to calculate +e use of fuzzy prin-cipal component analysis combined with TOPSIS can ob-jectively select regional collaborative innovation indicatorswhich has higher accuracy simpler principles and moreobjective conclusions and when the indicators increase thismethod performs data processing Effective decision-makinghas more advantages When there are a lot of data usestatistical software to process the data and implement thealgorithm throughMATLAB programming you can quicklyget scientific results so you can make decisions quickly Ofcourse this method can be applied not only to the evaluationof innovative service capabilities but also to other aspectssuch as supplier selection route selection and locationselection of distribution centers

+is article takes the biomedical industry as an examplein the regional collaborative innovation network It can befound that universities play an important role in the net-work which shows that companies tend to cooperate withuniversities to innovate and they must pay attention to andplay a role in the improvement of innovation service ca-pabilities +e important role of universities in the process isinnovation creation and dissemination +rough the indexconstruction and evaluation process of innovation servicecapacity it can be found that among the four regions in theYangtze River Delta Shanghai Jiangsu Province ZhejiangProvince and Anhui Province Shanghai has the strongestinnovation service capacity followed by Zhejiang Province+en came Jiangsu Province and finally Anhui Provinceand the conclusions of the study are in good agreement withthe actual situation in the Yangtze River Delta

52 Suggestions Finally according to the research conclu-sion of this paper the following two countermeasures andsuggestions are proposed to enhance the innovation servicecapability

Table 2 Expert survey

First-level indicators Secondary indicatorsShanghai Jiangsu Zhejiang Anhui

Name Weights Name Weights

Regional collaborative innovation investment [17 23]

Enterprise 50 128 130 110 140Efficient 20 90 90 90 80

RampD institutions 30 21 30 15 40Government 37 21 30 15 40

Regional collaborative innovation output [11 18] Results 35 80 120 170 99Income 30 34 50 60 30

Assistance in regional collaborative innovation [6 9] Economic basis 26 34 50 60 30Resident life 14 23 11 15 20

Table 3 Weighted synthesis of secondary indicators

First-level indicatorsShanghai Jiangsu Zhejiang Anhui

Name WeightsRegional collaborative innovation investment [17 23] 413956 4008919 409547 4186353Regional collaborative innovation output [11 18] 3708671 2616658 3915287 4184066Assistance in regional collaborative innovation [6 9] 4016341 4853234 3064865 4326791


First of all is the optimization suggestions on the inno-vation level of industry-university-research cooperation theimprovement of regional collaborative innovation capabilitiesneeds to be optimized from the perspective of regional andcollaborative innovation environments strengthen regionalcooperation increase the exchange and cooperation of in-novations avoid overlapping information and enjoy thesupport of multiple policies and multiple innovation envi-ronments At the same time Shanghai as a leader in theeconomic development of the Yangtze River Delta shouldplay its leading role in creating a globally influential scientificand technological innovation center and realize the commondevelopment of the region +e independent innovationactivities of universities enterprises and scientific researchinstitutions are not preferred +e optimization of the en-vironment requires many efforts +e core body of the in-dustry-university-research cooperative innovation network isan important participant and an important builder of thenetwork Financial institutions and intermediaries should alsoplay their roles to form an open and dynamic innovationenvironment an industry-university-research cooperationinnovation platform is established to maximize resourceutilization efficiency Innovation requires the cooperation andresource sharing of the core and related subjects so a matureoperating mechanism is needed to integrate the resources ofuniversities enterprises scientific research institutions gov-ernments financial institutions and intermediary institutionsto optimize the efficiency of resource utilization so estab-lishing a collaborative innovation platform is crucial

Secondly the government should optimize from thelevel of policies and regulations introduce correspondingencouragement policies and give more preferential taxpolicies to promote the creation and development of in-novation In addition to supporting and coordinatingfunctional RampD transformation platforms in addition tooptimization at the legal level online and offline platformscan be established combined with existing advanced in-formation technology so that the main body of the industry-university-research cooperation innovation network canbetter share resources and technology a correspondingbiomedical RampD and transformation platform is establishedto help companies innovate better and promote fastermarketization of innovations +e government plays animportant role in this process because the public serviceplatform must protect public welfare and encourage theresearch and development of shared technologies so thegovernment plays a vital role in it

Data Availability

+e data involved in this article were all from the ChinaStatistical Yearbook the China Science and TechnologyYearbook and the statistical yearbooks of various provincesand cities Among them the data in Figure 2 come from thepatent search database of the China Intellectual Property Office+e data used to support the findings of this study weresupplied by author under license and so cannot be made freelyavailable Requests for access to these data should be made to[Xiao-min Gu guxiaominlixineducn]

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] I Kim ldquoManaging Korearsquos system of technological innova-tionrdquo Interfaces vol 23 no 6 pp 13ndash24 1993

[2] G Huber ldquoSynergies between organizational learning andcreativity amp innovationrdquo Creativity and Innovation Man-agement vol 7 no 1 pp 3ndash8 1998

[3] S Radosevic ldquoDefining systems of innovation A methodo-logical discussionrdquo Technology in Society vol 20 no 1pp 75ndash86 1998

[4] L Power ldquo+e missing link Technology investment andproductivityrdquo Review of Economics and Statistics vol 80no 2 pp 300ndash313 1998

[5] B Morris ldquoHigh technology development Applying a socialnetwork paradigmrdquo Journal of New Business Ideas and Trendsvol 4 no 1 pp 45ndash59 2006

[6] I De Noni L Orsi and F Belussi ldquo+e role of collaborativenetworks in supporting the innovation performances oflagging-behind European regionsrdquo Research Policy vol 47no 1 pp 1ndash13 2018

[7] A Marasco M De Martino F Magnotti and A MorvilloldquoCollaborative innovation in tourism and hospitality Asystematic review of the literaturerdquo International Journal ofContemporary Hospitality Management vol 30 no 6pp 2364ndash2395 2018

[8] F Caviggioli ldquoTechnology fusion Identification and analysisof the drivers of technology convergence using patent datardquoTechnovation vol 55-56 no 6 pp 22ndash32 2016

[9] S Han G M Yoo and S Kwak ldquorsquoA comparative analysis ofregional innovation characteristics using an innovation actorframeworkrdquo Science Technology and Society vol 23 no 1pp 137ndash162 2018

[10] C Lindsay P Findlay J McQuarrie M BennieE D Corcoran and R Van Der Meer ldquoCollaborative in-novation new technologies and work redesignrdquo Public Ad-ministration Review vol 78 no 2 pp 251ndash260 2018

[11] L Zhen ldquoTactical berth allocation under uncertaintyrdquo Eu-ropean Journal of Operational Research vol 247 no 3pp 928ndash944 2015

[12] D C Bello L P Radulovich R G Javalgi R F Scherer andJ Taylor ldquoPerformance of professional service firms fromemerging markets role of innovative services and firm ca-pabilitiesrdquo Journal of World Business vol 51 no 3pp 413ndash424 2016

[13] O F Bustinza E Gomes F Vendrell-Herrero and T BainesldquoProduct-service innovation and performance +e role ofcollaborative partnerships and R amp D intensityrdquo R amp DManagement vol 49 no 1 pp 33ndash45 2019

[14] L Zhen ldquoModeling of yard congestion and optimization ofyard template in container portsrdquo Transportation ResearchPart B Methodological vol 90 pp 83ndash104 2016

[15] V Jayaraman and Z Liu ldquoAligning governance mechanismswith task features to improve service capabilities---an empiricalstudy of professional service outsourcing in Indiardquo OperationsManagement Research vol 12 no 1-2 pp 19ndash39 2019

[16] H Hakansson and I Snehota ldquoDeveloping relationships inbusiness networksrdquo Journal of Purchasing pp 1ndash261 1995

[17] R P J Rajapathirana and Y Hui ldquoRelationship betweeninnovation capability innovation type and firm


performancerdquo Journal of Innovation amp Knowledge vol 3no 1 pp 44ndash55 2018

[18] C L Hwang and K Yoon ldquoMultiple attribute decisionmakingrdquo Lecture Notes in Economics ampMathematical Systemsvol 404 no 4 pp 287-288 1981


influencing factors In terms of research perspectives theperspectives of papers and patents strategic emergingindustries and industrial ecosystems are introduced [6]+e research on the relationship between regional col-laborative innovation and innovation performance focuseson the evaluation of cross-regional system innovationcapability [7] +e research on the influencing factors ofregional collaborative innovation is carried out from theperspective of collaborative cooperation tendency inno-vation driving factors and the cooperation relationship ofinnovation subjects [8 9] +e domestic scholarsrsquo researchon cross-regional collaborative innovation ability mainlyfocuses on the evaluation of innovation ability the researchon the influencing factors and mechanism and mode ofinnovation ability +e evaluation of cross-regional col-laborative innovation capability provides different insightsfrom different perspectives covering research methodssuch as dynamic evaluation methods comparative analysismethods DEA and Malmquist index [10 11] +e researchon the influencing factors of cross-regional collaborativeinnovation capability has analysed its influencing factorsfrom different research perspectives including policyconditions network development resource investmentexternal learning and communication Some scholars havealso explored the mechanism and model of cross-regionalcollaborative innovation starting from the perspective ofsynergetic undertaking industrial transfer and technologydiffusion

Innovative service capability refers to the comprehensiveevaluation of the effect of a service innovation activity by anenterprise +e innovative service capability not only reflectsthe effectiveness of the organizationrsquos operations and marketcompetition but also reflects the projected development leveland actual effect of the organizationrsquos projects In recentyears research on innovative service capabilities has mostlyfocused on service-oriented enterprises and manufacturingindustries that provide products and services at the sametime [12 13] In order to achieve effective market compe-tition not only service-oriented enterprises andmanufacturing-oriented enterprises but also high-tech en-terprises also strive to provide customers with perfect ser-vices and constantly carry out service innovation activities inorder to improve the service quality of enterprises therebyattracting and retaining customers and stabilize or expandthe market [14 15] In addition under the leadership ofregional collaborative innovation whether an enterprisersquosinnovation service capability can be improved is crucial tothe overall performance of the enterprise

It can be seen by combing the relevant research at homeand abroad that the existing literature provides a basicanalysis framework for the expansion of innovation servicecapabilities and sustainable development at the practicallevel but there are relatively few studies on regional in-novation service capabilities and the existing evaluationindicators +e synergy between innovation elements in thesystem has not been considered One of the purposes of themeasurement and evaluation of innovation service capacityis to form a more effective governance mechanism andmodel to promote the development of interregional system

innovation so it is necessary to study the evaluation ofinnovation service capacity

Based on the current status of regional collaborativeinnovation development this study is dedicated to buildingan evaluationmodel for innovation service capabilities Firstthis study uses fuzzy principal component analysis to refinequantitative and qualitative indicator data for innovationservice capability selection and calculates index weightsSecond this study uses TOPSIS to assist in the evaluation ofinnovative service capabilities Due to the large amount ofdata in this article this study was implemented usingMATLAB programming Finally through a comparativeanalysis of the results this article obtained an optimizationplan for improving innovation service capabilities andproposed countermeasures and suggestions on how to guidethe flow of innovation elements and improve regionalcollaborative innovation

2 Evaluation Index System Construction andEvaluation Method

21 Regional Collaborative Innovation Network Citing theARA business network model proposed by Hakansson andSnehota [16] (Figure 1 combined with the relationshipbetween actors and social networks involved in social net-work analysis a regional collaborative innovation network isdefined +e commercial network contains three elementsparticipants resources and activities It can be seen that ifyou want to research a network you must first define thenetwork and secondly define the participants (or actors)resources and activities (social relations) +e resources andactivities here can be collectively referred to as relationshipsand they have an inseparable relationship with the partic-ipants In addition there are relationships among partici-pants resources and activities In order to facilitatemeasurement they are called relationships here As a resultthe participants and relationships of a network are definedand the boundaries of the network are clearly defined

Participants in collaborative innovation networks usu-ally cover enterprises universities scientific research insti-tutions intermediary services governments etc but thecore network of cooperative innovation networks mainlyincludes enterprises universities and scientific researchinstitutions networks composed of governments interme-diary services etc are marginal network which can also becalled a related network +e main research of this study isthe core network that is the main body of the network isenterprises universities and scientific research institutions

+e regional collaborative innovation network studied inthis paper selects the biopharmaceutical industry in thehigh-tech industry and builds a collaboration based on therelationship between companies universities and scientificresearch institutions in the biopharmaceutical industry andthe application of patent (national invention patents andutility models) innovation network +e results of the visualanalysis of the development of the biological medicine in-dustry in the Yangtze River Delta are shown in Figure 2

It can be seen from Figure 2 that the innovation ability ofuniversities in the collaborative innovation network of the








Actor

ActivitiesResources


jointly


resources





Business network









3 Model Principle



ηij aij

1113944n

i1 aij1113872 11138732

1113969 where i 1 2 n

j 1 2 k

(1)















Government














p


mj1 μj reaches a






pmax minus pmin+ aj

qj minus qmin

qmax minus qmin

(3)



wij B pj qj1113960 11139611113872 1113873

1113944m

j1B pj qj1113960 11139611113872 1113873 i 1 2 n (4)


βi wijμj

1113944m

j1wijμj

i 1 2 n (5)




XlowastT


1113936

Ni1 (vlowastij )2

1113969 i 1 2 n j 1 2 m +e



B ATW




⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (6)



B+

maxi

bij | j isin J1113876 1113877 b+1 b

+2 b

+j b

+m1113960 1113961 i 1 2 n

Bminus

mini


minus2 b

minusj b

minusm1113960 1113961 i 1 2 n

(7)


s+i

1113944

m

j1bij minus b

+j1113872 1113873

2

11139741113972

sminusi

1113944

m

j1bij minus b

minusj1113872 1113873

2

11139741113972

(8)


Ci s

minusi

sminusi + s

+i

i 1 2 n 0leCi le 1 (9)



4 Case Study





a1 095 W1 (03339 0 04965 01696) β1 (05299 0 03836 00865)

a2 076 W2 (03361 0 04834 01805) β2 (05340 0 03739 00921)

a3 082 W3 (03354 0 04875 01771) β3 (05327 0 03770 00903)

a4 065 W4 (03373 0 04762 01865) β4 (05362 0 03686 00952)

(10)




V

976278 763622 799790

401815 1128293 374480

94977 413866 482996

896354 372349 705447

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (11)


6i1 (vlowastij )2

1113969



B ATW

02873 00462 02367

01192 00354 01080

00281 00116 01405

02669 00416 02006

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (12)

Among them W

05299 00865 0383605340 00921 0373905327 00903 0377005362 00952 03686

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ are the



ibij|j isin J] [b+

1 b+2

b+3 ] i 1 2 4 get

B+

03356 02367 004621113858 1113859 (13)


From Bminus [mini


2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)


i 1113936

3j1 (vij minus v+

j )21113969


s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936


j )21113969


s+

03618 01535 01537 032201113858 1113859 (16)


i sminusi + s+


C 08822 03785 08055 032171113858 1113859 (17)





















Data Availability




References




























Actor

ActivitiesResources


jointly


resources





Business network









3 Model Principle



ηij aij

1113944n

i1 aij1113872 11138732

1113969 where i 1 2 n

j 1 2 k

(1)















Government














p


mj1 μj reaches a






pmax minus pmin+ aj

qj minus qmin

qmax minus qmin

(3)



wij B pj qj1113960 11139611113872 1113873

1113944m

j1B pj qj1113960 11139611113872 1113873 i 1 2 n (4)


βi wijμj

1113944m

j1wijμj

i 1 2 n (5)




XlowastT


1113936

Ni1 (vlowastij )2

1113969 i 1 2 n j 1 2 m +e



B ATW




⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (6)



B+

maxi

bij | j isin J1113876 1113877 b+1 b

+2 b

+j b

+m1113960 1113961 i 1 2 n

Bminus

mini


minus2 b

minusj b

minusm1113960 1113961 i 1 2 n

(7)


s+i

1113944

m

j1bij minus b

+j1113872 1113873

2

11139741113972

sminusi

1113944

m

j1bij minus b

minusj1113872 1113873

2

11139741113972

(8)


Ci s

minusi

sminusi + s

+i

i 1 2 n 0leCi le 1 (9)



4 Case Study





a1 095 W1 (03339 0 04965 01696) β1 (05299 0 03836 00865)

a2 076 W2 (03361 0 04834 01805) β2 (05340 0 03739 00921)

a3 082 W3 (03354 0 04875 01771) β3 (05327 0 03770 00903)

a4 065 W4 (03373 0 04762 01865) β4 (05362 0 03686 00952)

(10)




V

976278 763622 799790

401815 1128293 374480

94977 413866 482996

896354 372349 705447

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (11)


6i1 (vlowastij )2

1113969



B ATW

02873 00462 02367

01192 00354 01080

00281 00116 01405

02669 00416 02006

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (12)

Among them W

05299 00865 0383605340 00921 0373905327 00903 0377005362 00952 03686

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ are the



ibij|j isin J] [b+

1 b+2

b+3 ] i 1 2 4 get

B+

03356 02367 004621113858 1113859 (13)


From Bminus [mini


2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)


i 1113936

3j1 (vij minus v+

j )21113969


s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936


j )21113969


s+

03618 01535 01537 032201113858 1113859 (16)


i sminusi + s+


C 08822 03785 08055 032171113858 1113859 (17)





















Data Availability




References



























3 Model Principle



ηij aij

1113944n

i1 aij1113872 11138732

1113969 where i 1 2 n

j 1 2 k

(1)















Government














p


mj1 μj reaches a






pmax minus pmin+ aj

qj minus qmin

qmax minus qmin

(3)



wij B pj qj1113960 11139611113872 1113873

1113944m

j1B pj qj1113960 11139611113872 1113873 i 1 2 n (4)


βi wijμj

1113944m

j1wijμj

i 1 2 n (5)




XlowastT


1113936

Ni1 (vlowastij )2

1113969 i 1 2 n j 1 2 m +e



B ATW




⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (6)



B+

maxi

bij | j isin J1113876 1113877 b+1 b

+2 b

+j b

+m1113960 1113961 i 1 2 n

Bminus

mini


minus2 b

minusj b

minusm1113960 1113961 i 1 2 n

(7)


s+i

1113944

m

j1bij minus b

+j1113872 1113873

2

11139741113972

sminusi

1113944

m

j1bij minus b

minusj1113872 1113873

2

11139741113972

(8)


Ci s

minusi

sminusi + s

+i

i 1 2 n 0leCi le 1 (9)



4 Case Study





a1 095 W1 (03339 0 04965 01696) β1 (05299 0 03836 00865)

a2 076 W2 (03361 0 04834 01805) β2 (05340 0 03739 00921)

a3 082 W3 (03354 0 04875 01771) β3 (05327 0 03770 00903)

a4 065 W4 (03373 0 04762 01865) β4 (05362 0 03686 00952)

(10)




V

976278 763622 799790

401815 1128293 374480

94977 413866 482996

896354 372349 705447

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (11)


6i1 (vlowastij )2

1113969



B ATW

02873 00462 02367

01192 00354 01080

00281 00116 01405

02669 00416 02006

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (12)

Among them W

05299 00865 0383605340 00921 0373905327 00903 0377005362 00952 03686

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ are the



ibij|j isin J] [b+

1 b+2

b+3 ] i 1 2 4 get

B+

03356 02367 004621113858 1113859 (13)


From Bminus [mini


2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)


i 1113936

3j1 (vij minus v+

j )21113969


s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936


j )21113969


s+

03618 01535 01537 032201113858 1113859 (16)


i sminusi + s+


C 08822 03785 08055 032171113858 1113859 (17)





















Data Availability




References
























p


mj1 μj reaches a






pmax minus pmin+ aj

qj minus qmin

qmax minus qmin

(3)



wij B pj qj1113960 11139611113872 1113873

1113944m

j1B pj qj1113960 11139611113872 1113873 i 1 2 n (4)


βi wijμj

1113944m

j1wijμj

i 1 2 n (5)




XlowastT


1113936

Ni1 (vlowastij )2

1113969 i 1 2 n j 1 2 m +e



B ATW




⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (6)



B+

maxi

bij | j isin J1113876 1113877 b+1 b

+2 b

+j b

+m1113960 1113961 i 1 2 n

Bminus

mini


minus2 b

minusj b

minusm1113960 1113961 i 1 2 n

(7)


s+i

1113944

m

j1bij minus b

+j1113872 1113873

2

11139741113972

sminusi

1113944

m

j1bij minus b

minusj1113872 1113873

2

11139741113972

(8)


Ci s

minusi

sminusi + s

+i

i 1 2 n 0leCi le 1 (9)



4 Case Study





a1 095 W1 (03339 0 04965 01696) β1 (05299 0 03836 00865)

a2 076 W2 (03361 0 04834 01805) β2 (05340 0 03739 00921)

a3 082 W3 (03354 0 04875 01771) β3 (05327 0 03770 00903)

a4 065 W4 (03373 0 04762 01865) β4 (05362 0 03686 00952)

(10)




V

976278 763622 799790

401815 1128293 374480

94977 413866 482996

896354 372349 705447

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (11)


6i1 (vlowastij )2

1113969



B ATW

02873 00462 02367

01192 00354 01080

00281 00116 01405

02669 00416 02006

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (12)

Among them W

05299 00865 0383605340 00921 0373905327 00903 0377005362 00952 03686

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ are the



ibij|j isin J] [b+

1 b+2

b+3 ] i 1 2 4 get

B+

03356 02367 004621113858 1113859 (13)


From Bminus [mini


2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)


i 1113936

3j1 (vij minus v+

j )21113969


s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936


j )21113969


s+

03618 01535 01537 032201113858 1113859 (16)


i sminusi + s+


C 08822 03785 08055 032171113858 1113859 (17)





















Data Availability




References






















4 Case Study





a1 095 W1 (03339 0 04965 01696) β1 (05299 0 03836 00865)

a2 076 W2 (03361 0 04834 01805) β2 (05340 0 03739 00921)

a3 082 W3 (03354 0 04875 01771) β3 (05327 0 03770 00903)

a4 065 W4 (03373 0 04762 01865) β4 (05362 0 03686 00952)

(10)




V

976278 763622 799790

401815 1128293 374480

94977 413866 482996

896354 372349 705447

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (11)


6i1 (vlowastij )2

1113969



B ATW

02873 00462 02367

01192 00354 01080

00281 00116 01405

02669 00416 02006

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (12)

Among them W

05299 00865 0383605340 00921 0373905327 00903 0377005362 00952 03686

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ are the



ibij|j isin J] [b+

1 b+2

b+3 ] i 1 2 4 get

B+

03356 02367 004621113858 1113859 (13)


From Bminus [mini


2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)


i 1113936

3j1 (vij minus v+

j )21113969


s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936


j )21113969


s+

03618 01535 01537 032201113858 1113859 (16)


i sminusi + s+


C 08822 03785 08055 032171113858 1113859 (17)





















Data Availability




References






















From Bminus [mini


2 bminus3 ] i 1 2

4 get

Bminus

00281 minus00132 001161113858 1113859 (14)


i 1113936

3j1 (vij minus v+

j )21113969


s+

00483 02521 03241 007771113858 1113859 (15)

From sminusi

1113936


j )21113969


s+

03618 01535 01537 032201113858 1113859 (16)


i sminusi + s+


C 08822 03785 08055 032171113858 1113859 (17)





















Data Availability




References
























Data Availability




References






















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