researcharticle research on supplier evaluation in a green...

Research ArticleResearch on Supplier Evaluation in a Green Supply Chain

Qiang Hou and Lei Xie

Department of Management Shenyang University of Technology Shenyang 110870 China

Correspondence should be addressed to Qiang Hou 18904046277163com

Received 24 November 2018 Revised 28 February 2019 Accepted 5 March 2019 Published 27 March 2019

Academic Editor Ewa Pawluszewicz

Copyright copy 2019 Qiang Hou and Lei Xie This 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 is properlycited

The supplier is considered to be attractive under green supply chain management supplier evaluation is also confronted with aserious challenge Based on this background this paper studies green supplier evaluation and selection with weights unknown inhesitant fuzzy sets and presents evaluation indexes by the DEMATEL method On the basis of the Euclidean distance hesitancydegree is used to construct the improved type signed distance At last the paper calculates relative closeness to rank green suppliersby the improved TOPSISmethod and compares the results of the traditional algorithm and SAWmethodThe result of the exampleshows that the algorithm has practicability and a dipartite degree

1 Introduction

With the increasing trend of environmental awareness andthe change of competitive factor in enterprises a greensupply chain has developed rapidly under environmentalmanagement in recent yearsThe supplier is located upstreamin a green supply chain and it can realize transmissiondownstream Meanwhile the supplier has the characteristicof cost increase in posttreating The green supplier which islocated upstream can take into account both environmentand benefit (Luo and Peng [1] Humphreys (2003) [2])Thus on the background of a green supply chain supplierevaluation becomes an extremely important research sub-ject

The current research situation of green supplier evalu-ation pays more attention to the evaluation index systemand design method It can be seen that the evaluation indexsystem ismainly involved in factors of suppliersrsquo coordinationandmatching of demanding Somany literatures have studiedthe evaluation index system In fact it has relevance highlyamong indexes Because of the high correlation degree somefactors have been enhanced and others have been weakened

From the point of view of the evaluation method itmainly includes seven factors of the valuator evaluationobjective evaluation object evaluation index evaluationcriterion index weight and evaluation method As the

most important foundation of index attribute measure therelationships of value are grey fuzzy Actually the indexexpression of supplier attribute is highly uncertain andfuture expectation of experts is more uncertain based on thelimitation of information

Based on the above analysis this paper is mainly tostudy the improvement method which includes correlationbetween indexes and hesitant fuzzy sets of index measure-ment To be specific the study proposes to measure thecorrelation of indexes by the DEMATEL method On theother hand it applies to solve the problem of attributemeasurement by using a hesitant fuzzy set

The innovative points of this paper are the following(1) according to the relations of indexes the curtailment ismore effective (2) this paper projects the TOPSIS method todeal but the hesitancy degree is higher when the deviation isbigger It will affect the distance between hesitant fuzzy setsThus this paper makes innovations in hesitant distance

The organizational structure of the remainder of thepaper is the following Section 2 presents the problemdescription and evaluation process Section 3 shows the indexselection method Section 4 proposes the index evaluationandmeasurement in a hesitant fuzzy set Section 5 carries outa case study Section 6 discusses the analysis for the resultFinally Section 7 draws a conclusion

HindawiDiscrete Dynamics in Nature and SocietyVolume 2019 Article ID 2601301 14 pageshttpsdoiorg10115520192601301

2 Discrete Dynamics in Nature and Society

2 Problem Description andEvaluation Process

This paper discusses the existing problems of green supplierevaluation in the multiple attributes And the hesitant fuzzyset can solve problems of the fuzzy information and theuncertain index system the DEMATEL method can deter-mine the evaluation index Based on the above methodsthe study shows the problem description and the evaluationprocess

21 Problem Description Under the background of a greensupply chain determining the alternative suppliers is neces-sary firstly Then it can determine the attribute of evaluationindex by the DEMATEL method and the structure decisionmatrix under a hesitant fuzzy set Based on the abovedescription the paper defines the symbols and interpretationas follows

Definition 1 119860 = 1198601 1198602 sdot sdot sdot 119860 119894 | 119894 = 1 2 sdot sdot sdot 119899 denotesthe set of suppliers and 119860 119894 is the 119894119905ℎ green supplier

Definition 2 119874 = 1198741 1198742 sdot sdot sdot 119874119895 | 119895 = 1 2 sdot sdot sdot 119898 denotesthe set of attributes and 119874119895 is the 119895119905ℎ attributeDefinition 3 120596 = 1205961 1205962 sdot sdot sdot 120596119895 | 119895 = 1 2 sdot sdot sdot 119898 denotesthe set of attribute weights and 120596119895 is the 119895119905ℎ attribute weightwhere 120596119895 isin [0 1] and sum119898119895=1 120596119895 = 1Definition 4 ℎ119894119895 is the hesitant fuzzy set and it representsall evaluation values in 119874119895 of 119860 119894 and this paper structuresa hesitant fuzzy set decision matrix 119867 = (ℎ119894119895)119899times119898 and ℎ119894119895 =120574120582119894119895 | 120582 = 1 2 sdot sdot sdot 119897 where 120574120582119894119895 is expert estimation

Definition 5 Δ 119894119895 is the hesitancy degree in the scheme and0 le Δ 119894119895 le 1(119894 = 1 2 sdot sdot sdot 119899 119895 = 1 2 sdot sdot sdot 119898)Definition 6 119889(1198671 1198672) represents the Euclidean distance oftwo hesitant fuzzy sets

Definition 7 119889lowast(119867119894 119867119895) represents the improvement distanceof adding hesitancy degree

Definition 8 119888(119860 119894) represents the relative closeness and 119894 =1 2 sdot sdot sdot 119899Definition 9 B = (bij)itimesj is the direct effect matrix in theDEMATELmethod in which bij represents expert evaluationand is written by a 5-degree scoring standard bij is giveninteger score of 0-4 representing ldquoNo influence(0)rdquo ldquoLowinfluence(1)rdquo ldquoGeneral influence(2)rdquo ldquoHigh influence(3)rdquoand ldquoVery high influence(4)rdquo bij represents correlationdegree from index ith to index jth And D is the standardizedmatrix of matrix B

Definition 10 T is the total effect matrix in the DEMATELmethod and T = (tij)itimesj = D(E minus D)minus1

Definition 11 fi represents effect degree and fi = sumnj=1 tij (i =1 2 sdot sdot sdot n)

Definition 12 ei represents affected degree and ei =sumnj=1 tji (i = 1 2 sdot sdot sdot n)

Definition 13 mi represents centrality degree and mi = fi +ei (i = 1 2 sdot sdot sdot n)Definition 14 ni represents cause degree and ni = fi minus ei (i =1 2 sdot sdot sdot n)22 13e Evaluation Process The purpose of this paper isthat using fuzzy language evaluates the green supplier theprocess involves method selection weight determinationand index selection In order to solve the problems this paperdetermines the evaluation index by the DEMATEL methodredefines the improved distance formula based on a hesitantfuzzy set and extends a new evaluation method Figure 1shows the system of supplier evaluation

Based on the analysis the algorithm of the evaluationsystem is summarized as follows

Step 1 Formulate appropriate green suppliers and attributesby using the DEMATEL method and denote them by 119860 =1198601 1198602 sdot sdot sdot 119860 119894 | 119894 = 1 2 sdot sdot sdot 119899 and 119874 = 1198741 1198742 sdot sdot sdot 119874119895 |119895 = 1 2 sdot sdot sdot 119898 respectivelyStep 2 Construct hesitant fuzzy decision matrix 119867 =(ℎ119894119895)119899times119898Step 3 Calculate positive ideal solution119860+ and negative idealsolution 119860minusStep 4 Solve the attribute hesitancy degree of each supplierand redefine the new distance

Step 5 Adopt the maximizing deviation method to deter-mine attribute weight 120596119895Step 6 Calculate distances between the green supplier andpositive-negative ideal solution

Step 7 Compute the relative closeness 119888(119860 119894)Step 8 Rank 119888(119860 119894)(119894 = 1 2 sdot sdot sdot 119899) and select the optimalgreen supplier

3 Construct the Evaluation Index System

In Step 1 the index system is the evaluation basis of thesupplier thus the index is very important On the other handappropriate indexes play an important role in the evaluationgreen supplier

31 Construct the Initial Index The index is the importantelement to evaluate the supplier Dickson (1996) [3] is themost influential in supplier evaluation he evaluated theevaluation indexes of 23 suppliers and indicated that the

Discrete Dynamics in Nature and Society 3

Construct team of expertevaluation

Identify potential greensuppliers Evaluate green suppliers

1 Determine theevaluation index2 Expression of index

21 Construct hesitantfuzzy decision matrix

3-4 Calculate hesitancydegree and redefineEuclidean distance

Maximizing deviationmethod

5 Compute the indexweight of addinghesitancy degree

6-7 Solve closenessdegree TOPSIS method

8 Rank suppliers andselect the best supplier

14 Get the main indexes

13 Calculate centralitydegree and cause degree

Calculate relevancedegree

12 Establish indexsystem and compute

influence matrix

11 Put outquestionnaires to experts

and literature review

Delphi method andliterature method

e evaluation method DEMATEL

Figure 1 The evaluation process of a green supplier

important indexes are quality and historical performance aswell as delivery period To face the current environmentalsituation Handfield et al (2002) [4] Shaw et al (2012) [5]and Hsu et al (2013) [6] added the green evaluation indexfor instance greenhouse gas emission and green purchasingBased on the above He et al (2018) [7] put forward 18 indexesof qualitative and quantitative evaluation It can be seen thatevaluation indexes are various

Index selection should follow principles which includesystematicness overall science stability flexibility andbrevity Based on the research and principles this paperproposes the initial index by theDelphimethod and literaturemethod

The Delphi method can provide a more reliable indexBriefly the Delphi method can make expert opinions ininduction and arrangement scientifically and repeat verifi-cation until getting centralized indexes On the one handthe literature method can also analyze and epurate theevaluation index by collecting literatures On the other handby combining the two methods the initial index set isobtained completely

32 Index Reduction the DEMATEL Method Obviously theevaluation indexes have high relevance The initial index isfar from being refined This paper is mainly for an enterprisewhich also seeks green and high efficiency The DEMATEL(Decision-Making Trial and Evaluation Laboratory) (Gabusand Fontela [8]) model generally uses the knowledge and

experience of an expert to select main indexes particularly itis more useful to a system of an element uncertainty relationSo it can select the optimal supplier of a green industryenterprise by using the DEMATEL method And the steps ofDEMATEL are following

Firstly through expert interview and literature retrievalit aims at experts and enterprises with a questionnaireAnd then it can finish indexesrsquo statistic by returning thequestionnaire Combining with statistical data and expertadvice the evaluation index can be divided into first-gradeindexes and second-grade indexes

Then it can establish the direct effect matrix B = (bij)itimesjIn order to establish the direct effect matrix it is necessary toset up an assessment group then the correlation degree canbe defined by an analysis and discussion And the interactiondegree of the index is given integer score of 0-4 Then usingformula (1) can get a standard matrix D

D = 1max1leilensumn

j=1 bijB (1)

bij represents the correlation degree from index ith toindex jth

Thirdly according to matrix D it can get the totalinfluence matrix T effect degree fi and affected degree ei byformulas Meanwhile centrality degree mi and cause degreeni can be calculated And it can get cause-effect relationships

Finally we can recognize the rank of indexes by cause-effect relationships Then it can obtain the main indexes


4 Supplier Evaluation Method

This paper constructs the model from four aspects First ina previous paper it could gain the main indexes accordingto the correlation degree among indexes by the DEMATELmethod Then in multiple-attribute decision-making thehesitancy degree of evaluation schemes is higher and thedistance is bigger Thus this paper redefines the distanceformula Thirdly in order to avoid the subjective effect themethod adopts the maximizing deviation method to deter-mine weights 120596 Finally the improved traditional TOPSISmethod can evaluate and select optimal suppliers

41 Improvement Distance Metric In a hesitant fuzzy set thetraditional Euclidean distance has its limitation Particularlythe evaluation process shows a hesitancy degree Thus howto define the new distance metric is worth studying

411 Measure Index Hesitant Fuzzy Set In 1965 ProfessorZadeh [9] brought forward the concept of a fuzzy set hethought a set includes two states support and oppositionin other words a fuzzy set is characterized by a member-ship degree and nonmembership degree Thereafter scholarshave paid more attention to fuzzy sets Moreover hesitantfuzzy sets are multidimensional observers which has beenconsidered first by Molaei (2009) [10] as an extension of aone-dimensional observer (Molaei (2004) [11]) Atanassov(1986) [12] proposed the intuitionistic fuzzy set theorythe new theory added hesitancy degree which respects theneutralizing attitude for judging Torra andNarukawa (2009)[13] suggested a hesitant fuzzy set that could describe thepossibility of each element In Step 2 actually it often showsinformation which makes investors hesitate when they aremaking decisions thus Xia and Xu (2011) [14] defined themathematical expression of a hesitant fuzzy set

Definition 15 It hypothesizes that 119909 = 1199091 1199092 sdot sdot sdot 119909119897 is anonempty set and a hesitant fuzzy set is denoted in

119867 = ⟨119909 ℎ (119909)⟩ | 119909 isin 119883 (2)

ℎ(119909) is the hesitant fuzzy element it denotes the degreethat the scheme satisfies the attribute and ℎ(119909) isin [0 1] Thenthe hesitant fuzzy decision-making matrix is shown in

119867 =

[[[[[[[[

ℎ11 ℎ12 ℎ1119898ℎ21 ℎ22 ℎ2119898

dℎ1198991 ℎ1198992 ℎ119899119898

]]]]]]]] (3)

Themembership degree of a hesitant fuzzy set reflects thehesitancy degree The greater the deviation among elementsthe higher the hesitancy degree Based on this in Step 4Zhang and Xu (2015) [15] defined the hesitancy degree in ahesitant fuzzy set

Definition 16 For a hesitant fuzzy set 119867119894119895 = 120574120582119894119895 | 120582 =1 2 sdot sdot sdot 119897 119894 = 1 2 sdot sdot sdot 119899 119895 = 1 2 sdot sdot sdot 119898 120574120582119894119895 is 120582th of119867119894119895 andthe hesitancy degree of119867119894119895 is defined in

Δ = 1C119897

119897sum120582gt120590=1

10038161003816100381610038161003816120574120582 minus 12057412059010038161003816100381610038161003816 119894119891 119897 gt 10 119894119891 119897 = 1 (4)

where 119862119897 = (12)119897(119897 minus 1) 120574120582 isin [0 1] and 120574120590 isin [0 1] arethe smallest 120582119905ℎ and 120590119905ℎ in119867119894119895

Moreover distance measurement is widely applied inmany fields Xu and Xia (2011) [16] indicated the distance oftwo hesitant fuzzy sets based on the Euclidean distance

Definition 17 For two hesitant fuzzy sets 1198671 and 1198672119889(1198671 1198672) is the distance of two hesitant fuzzy sets119889 (1198671 1198672) = radic 1119897

119897sum119902=1

10038161003816100381610038161003816119867120582(119902)1 minus 119867120582(119902)2 100381610038161003816100381610038162 (5)

where 119867120582(119902)1 isin [0 1] and 119867120582(119902)2 isin [0 1] are the 119902119905ℎ valuein 1198671 and 1198672 respectively and they possess the followingproperties

(1) 0 le 119889(1198671 1198672) le 1(2) 119889(1198671 1198672)= 119889(1198672 1198671)(3) 119889(1198671 1198672) = 0 if and only if1198671=1198672

412 New Distance Metric Based on the fuzziness of infor-mation this paper employs a hesitant fuzzy set to deal withinformation Some literatures have adopted hesitant fuzzysets with various ways (Shi and Xiao (2018) [17] Wu and Cao(2012) [18]) And some have improved the hesitant fuzzy setsAdditionally the distance from the ideal point of TOPSIS isalways improved such as in Ran (2018) [19] and Lin et al(2018) [20] Actually the hesitancy degree is higher when thedeviation is bigger then the distance of two hesitant fuzzy setsbecomes larger accordingly And it can be aware of limitationin distance formula (5) This paper redefines the distanceformula in Step 4 as following in

119889lowast (119867119894 119867119895) = 119889 (119867119894 119867119895)(1 minus Δ 119894) (1 minus Δ 119895)= radic(1119897) sum119897119902=1

10038161003816100381610038161003816119867120582(119902)119894 minus 119867120582(119902)119895 100381610038161003816100381610038162(1 minus Δ 119894) (1 minus Δ 119895) (6)

Δ 119894 and Δ 119895 are the hesitancy degrees in schemes 119894 and119895 respectively and the value of the hesitancy degree inthe positive ideal solution and negative ideal solution is 0119889(119867119894 119867119895) is the Euclidean distance of two hesitant fuzzy sets119867119894 and 119867119895 And formula (6) should satisfy the followingproperties


(1) 119889lowast(119867119894 119867119895) ge 119889(119867119894 119867119895)(2) 119889lowast(119867119894 119867119895) = 119889lowast(119867119895 119867119894)(3) 119889lowast(119867119894 119867119895) = 0 if and only if119867119894 = 119867119895

Proof (1) 0 le Δ 119894 le 1 119889lowast(119867119894 119867119895) = 119889(119867119894 119867119895)(1 minus Δ 119894)(1 minusΔ 119895) ge 119889(119867119894 119867119895)(2) Because 119889(119867119894 119867119895) = 119889(119867119895 119867119894) therefore 119889lowast(119867119894119867119895) = 119889(119867119894 119867119895)(1 minus Δ 119894)(1 minus Δ 119895) = 119889(119867119895 119867119894)(1 minus Δ 119894)(1 minusΔ 119895) = 119889lowast(119867119895 119867119894)(3) If 119889lowast(119867119894 119867119895) = 0 119867120582(119902)1 = 119867120582(119902)2 thus 119867119894 = 119867119895 while

if 119867119894 = 119867119895 119889lowast(119867119894 119867119895) = 0 And 119889lowast(119867119894 119867119895) = 0 if and onlyif119867119894 = 11986711989542 A Method of Determining Attribute Weight Weightoccupies an important position in evaluation Referencing Xuand Zhang (2013) [21] we adopt the maximizing deviationmethod to determine attribute weight In Step 5 deviationformulas of what 119860 119894 is related to other schemes are followingin

119889lowast119894119895 (120596) = 119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) 120596119895119894 = 1 2 119899 119895 = 1 2 119898

(7)

where 119889lowast(ℎ119894119895 ℎ119896119895) = radic(1119897) sum119897119902=1 |ℎ120582(119902)119894119895 minus ℎ120582(119902)119896119895|2(1 minusΔ 119894119895)(1 minus Δ 119896119895) denotes the Euclidean distance of ℎ119894119895 and ℎ119896119895

Thuswe can construct the deviations of all schemes underthe condition 119874119895 isin 119874 in119889lowast119895 (120596) = 119899sum

119894=1

119889lowast119894119895 (120596)

= 119899sum119894=1

119899sum119896=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus ℎ120582(119902)119896119895

1003816100381610038161003816100381610038162(1 minus Δ 119894119895) (1 minus Δ 119896119895) 119895 = 1 2 119898

(8)

Based on this analysis we propose a nonlinear pro-gramming model that could determine weight vector 120596 andmaximum deviation The model is following in

max 119889lowast (120596) = 119898sum119895=1

119899sum119894=1

119899sum119896=1

120596119895119889lowast (ℎ119894119895 ℎ119896119895)st 120596119895 ge 0 119895 = 1 2 119898 119898sum

119895=1

120596119895 = 1(9)

In order to solve the model let

119891 (120596 120593) = 119898sum119895=1

119899sum119894=1

119899sum119896=1

120596119895119889lowast (ℎ119894119895 ℎ119896119895) + 1205932 (119898sum119895=1

120596119895 minus 1) (10)

Formula (10) denotes the Lagrangian function of con-straining the optimization problem and 120593 is a real number

and denotes the Lagrangian multiplier Thus we calculate thepartial differential

120597119891120597120596119895 =119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) + 120593120596119895 = 0 (11)

120597119891120597120593 = 12 (119898sum119895=1

1205962119895 minus 1) = 0 (12)

120596119895 is prepared from formula (11)

120596119895 = minussum119899119894=1sum119899119896=1 119889lowast (ℎ119894119895 ℎ119896119895)120593 119895 = 1 2 119898 (13)

Bringing formula (13) into formula (12) it can be obtainedin

120593 = minusradic 119898sum119895=1

( 119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895))2 (14)

Obviously 120593 lt 0 sum119899119894=1sum119899119896=1 119889lowast(ℎ119894119895 ℎ119896119895) denotes thedeviations of all schemes in attribute 119895

Then combining with (13) and (14) gives

120596119895 = sum119899119894=1sum119899119896=1 119889lowast (ℎ119894119895 ℎ119896119895)radicsum119898119895=1 (sum119899119894=1sum119899119896=1 119889lowast (ℎ119894119895 ℎ119896119895))2

(15)

For the sake of brevity we write 119863119895 =sum119899119894=1sum119899119896=1 119889lowast(ℎ119894119895 ℎ119896119895) 119895 = 1 2 sdot sdot sdot 119898 and simplify (15)

120596119895 = 119863119895radicsum119898119895=11198632119895 119895 = 1 2 119898 120596119895 isin [0 1] (119895 = 1 2 119898)

(16)

where 120596119895(119895 = 1 2 sdot sdot sdot 119898) is positive number and themodel has a unique solution Finally we make 120596119895 standard-ized as followed in

120596lowast119895 = 120596119895radicsum119898119895=1 120596119895 119895 = 1 2 119898 (17)

By solving the model optimal solution 120596 =(1205961 1205962 sdot sdot sdot 120596119898)119879 can be drawn

43 13e Evaluation Method the TOPSIS Method The mul-tiattribute decision-making method is involved in standard-ization of the decision matrix choice of attribute weight andalternative ranking In the above weight has already beenredefined Differentmethods of standardizing thematrix leadto different results Moreover the traditional methods areSAW (Simple Additive Weighting) [22] ELECTRE [23] andothers The methods of green supplier evaluation and selec-tion are various at present Briefly DEA (Saen (2010) [24]Azadeh (2010) [25]) AHP (Yang (2003) [26] Diego (2012)


[27]) fuzzy AHP (Shaw (2012) [5] Mangla (2017) [28])ANP (Saaty (1996) [29] Vinodh (2010) [30] Bakeshlou (2017)[31]) and TOPSIS (Hwang et al (1981) [32] Buyukozkan(2012) [33] Fallahpour (2017) [34]) are most widely usedin supplier selection But the TOPSIS method can makefull use of original data and the result of TOPSIS preciselyreflects the gap among suppliers And green supplier selectionis decision-making of fuzzy multiple attributes Generallythe above methods have a certain limitation and evaluationmechanisms have some defects Because of the uncertainand fuzzy information in the environment and the cognitiondifference in Steps 6 and 7 this paper will hold green supplierevaluation by the TOPSIS method under a hesitant fuzzy set

Attribute weights have been already determined In orderto overcome the drawback of losing integration informationeasily this paper redefines the improved type signed distanceformula Then we sequence the relative closeness betweeneach green supplier and ideal solution Finally the optimalsupplier can be selected

Under a hesitant fuzzy environment in Step 3119860+ and119860minusare the positive ideal solution and negative ideal solution asfollows

119860+ = ⟨119909119895max119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)+ (ℎ21)+ (ℎ1198971)+⟩ ⟨1199092 (ℎ12)+ (ℎ22)+ (ℎ1198972)+⟩ ⟨119909119898 (ℎ1119898)+ (ℎ2119898)+ (ℎ119897119898)+⟩

(18)

119860minus = ⟨119909119895min119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)minus (ℎ21)minus (ℎ1198971)minus⟩ ⟨1199092 (ℎ12)minus (ℎ22)minus (ℎ1198972)minus⟩ ⟨119909119898 (ℎ1119898)minus (ℎ2119898)minus (ℎ119897119898)minus⟩

(19)

According to (6) we calculate distance (119889lowast119894 )+ and (119889lowast119894 )minusbetween each green supplier and ideal solution

(119889lowast119894 )+ = 119898sum119895=1

119889lowast (ℎ119894119895 ℎ+119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus (ℎ120582(119902)119895 )+1003816100381610038161003816100381610038162(1 minus Δ 119894) (1 minus +) 119894 = 1 2 119899

(20)

(119889lowast119894 )minus = 119898sum119895=1

119889lowast (ℎ119894119895 ℎminus119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus (ℎ120582(119902)119895 )minus1003816100381610038161003816100381610038162(1 minus Δ 119894) (1 minus minus) 119894 = 1 2 119899

(21)

Then we can solve relative closeness between supplier 119860 119894and positive ideal solution 119860+

119888 (119860 119894) = (119889lowast119894 )minus(119889lowast119894 )+ + (119889lowast119894 )minus 119894 = 1 2 119899 (22)

where 0 lt 119888(119860 119894) lt 1 119894 = 1 2 sdot sdot sdot 119899 Based on themagnitude of closeness degree it can select the optimal greensupplier

5 A Case Study for Green Suppliers Evaluation

This paper takes green suppliers for example There are 4suppliers provided (119860 119894(119894 = 1 2 3 4)) in a green supplychain Through expert interview and literature retrievaland combining with statistical data and expert advice theevaluation index can be divided into 4 first-grade indexes and20 second-grade indexes as shown in Table 1

Then the direct effect matrix B is calculated by expertevaluation The matrix can make information put in order asshown in Table 2

Thus we can acquire the total influence matrix T Thecomputing formulas of the matrix result in the cause-effectrelationship which is presented in Table 3

From Table 3 it is significant that the equipment productqualification ratio and service satisfaction have high effectdegrees Among them equipment is highest because equip-ment is related to not only product quality and qualified ratebut also environmental pollution Meanwhile the indexeshave a lower centrality degree and cause degree includingthe information level staff quality energy consumption andldquothree-wasterdquo recycling rate After eliminating the secondaryindexes this paper would select 16 main evaluation indexesof the green supplier

Index selection should follow principles which includesystematicness overall science stability flexibility andbrevity Based on the research and principles this paperproposes the index system of the green supplier 16 evaluationindexes are shown in Figure 2 respectively

And suppliersrsquo indexes can be scored by experts afterobtaining the index system Evaluation information is shownin Table 4

Then the proposed approach of the improved type signeddistance in a hesitant fuzzy set is the following

In Step 1 suppliers and indexes are denoted by 119860 =1198601 1198602 1198603 1198604 and119874 = 1198741 1198742 sdot sdot sdot 11987416 | 119895 =1 2 sdot sdot sdot 16 respectivelyIn Step 2 we denote the hesitant fuzzy decision-making

matrix119867 = (ℎ119894119895)4times16 as in Table 4


Table 1 The evaluation index system of the green supplier

Evaluation objective Level indicators Secondary indicators

Evaluation index systemof green supplierselection

Product level Quality management system (O1)Relative price level (O2)

Equipment (O3)Product qualification ratio (O4)

Logistics cost (O5)Service level On-time delivery rate (O6)

Order completion rate (O7)Services response speed (O8)Service satisfaction (O9)

Development level Information level (O10)Profit growth rate (O11)

RampD input (O12)Corporate reputation (O13)

Staff quality (O14)Financial situation (O15)

Environmental competitiveness Exhaust gas emission (O16)Energy consumption (O17)

Cleaner production level (O18)ldquoThree-wasterdquo recycling rate (O19)Green enterprise image (O20)

Table 2 The direct effect matrix B of the green supplier

Index O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14 O15 O16 O17 O18 O19 O20O1 0 2 4 4 0 0 0 0 1 0 1 1 2 1 0 2 2 0 1 0O2 3 0 1 0 1 0 0 0 0 0 4 3 0 0 4 0 1 0 1 0O3 2 4 0 4 0 2 3 2 0 2 2 4 0 0 4 2 2 3 1 2O4 4 3 4 0 2 2 3 0 4 0 3 1 4 3 2 0 0 1 0 0O5 1 0 0 1 0 1 0 0 0 1 4 0 0 0 3 0 0 0 0 0O6 0 0 2 2 2 0 4 0 4 2 1 0 3 0 2 0 0 0 0 0O7 1 0 4 1 0 4 0 0 4 2 3 0 3 0 3 0 0 0 0 0O8 4 0 3 1 0 2 3 0 4 0 3 0 2 3 1 0 0 0 0 0O9 4 0 2 3 0 4 4 0 0 0 4 0 4 4 0 2 0 0 0 0O10 0 0 2 0 1 0 0 2 0 0 2 1 0 0 0 0 1 1 0 1O11 3 4 4 1 3 0 4 0 0 0 0 2 0 0 4 0 0 1 1 0O12 0 2 4 0 1 0 0 0 0 3 3 0 0 0 4 1 0 3 1 3O13 3 0 1 3 0 0 0 2 3 1 2 0 0 2 0 1 1 1 0 3O14 0 0 0 1 0 0 1 2 4 0 0 0 1 0 0 0 0 0 0 0O15 0 3 4 1 1 1 0 0 0 2 3 3 0 0 0 0 0 1 0 0O16 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 3 2 4 4O17 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2 4 3O18 0 0 2 0 0 0 1 0 0 0 1 1 0 0 2 4 4 0 3 4O19 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 4 3 0 4O20 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 4 4 0 4 0

In Step 3 we calculate the positive ideal solution 119860+ andnegative ideal solution 119860minus respectively119860+ = ⟨1199091 06 06 05 04⟩ ⟨1199092 05 06 08 09⟩ ⟨1199093 06 05 05 07⟩ ⟨1199094 05 06 07 09⟩

⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩


Table 3 The cause-effect relationship of the green supplier

Evaluation index Effect Affected Centrality Causedegree (fi) degree (ei) degree (mi) degree (ni)

O1 Quality management system 13020 14770 27790 -01750O2 Relative price level 10294 12872 23166 -02578O3 Equipment 21965 22783 44748 -00818O4 Product qualification ratio 21557 13253 34810 08304O5 Logistics cost 06581 06563 13144 00018O6 On-time delivery rate 13786 09162 22948 04624O7 Order completion rate 15961 13306 29267 02655O8 Services response speed 16362 04482 20844 11880O9 Service satisfaction 18683 11995 30678 06688O10 Information level 06564 07670 14234 -01106O11 Profit growth rate 15873 19612 35485 -03739O12 RampD input 13670 10711 24381 02959O13 Corporate reputation 13510 12392 25902 01118O14 Staff quality 06213 06765 12978 -00552O15 Financial situation 11584 17655 29239 -06071O16 Exhaust gas emission 07622 11726 19348 -04104O17 Energy consumption 06145 12672 18817 -06527O18 Cleaner production level 10914 10870 21784 00044O19 ldquoThree-wasterdquo recycling rate 07153 11618 18771 -04465O20 Green enterprise image 06856 13436 20292 -06580

⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)

In Steps 4 and 5 there are the results of attribute hesitancydegree and the improved type signed distance in Table 5 andTable 6 respectively

According to the distance the weight vector can becalculated

120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)

In Step 6 we compute the distances (119889lowast119894 )+ and (119889lowast119894 )minus fromeach supplier 119860 119894 to the positive-negative ideal solution byusing Eqs (25) and (26)

(119889lowast1 )+ = 03652(119889lowast2 )+ = 02999(119889lowast3 )+ = 04589(119889lowast4 )+ = 04695(119889lowast1 )minus = 04284

(119889lowast2 )minus = 04427(119889lowast3 )minus = 03110(119889lowast4 )minus = 03368

(25)

In Steps 7 and 8 we calculate the relative closeness 119888(119860 119894)values and rank them

119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)

1198602 ≻ 1198601 ≻ 1198604 ≻ 1198603 so 1198602 is the ideal supplier6 Result Analysis

Based on the proposed algorithm this part compares theresults of the improved TOPSIS and traditional TOPSIS

methods and studies the different multiattribute decision-makingmethods of the improvedTOPSIS and SAWmethodsBy comparing the results among the three methods the sameand different points and advantages can be found

61 13e Result of the Traditional TOPSIS Method The hesi-tant fuzzy set reflects the hesitancy degree of differences Anddeviations among elements are greater hesitancy degree ishigher Meanwhile Xu and Zhang (2013) [21] applied theideal point method and obtained attribute weight

120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)

By using the attribute weight it can get the closenessdegree as follows

(119889lowast1 )+ = 02595(119889lowast2 )+ = 02078(119889lowast3 )+ = 03843(119889lowast4 )+ = 04083(119889lowast1 )minus = 03693(119889lowast2 )minus = 03830(119889lowast3 )minus = 02092(119889lowast4 )minus = 01773

(28)

Through the closeness degree the result can be drawn

119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)

Then the ranking is 1198602 ≻ 1198601 ≻ 1198603 ≻ 1198604 and 1198602 is theideal supplier

62 13e Result of the SAW Method SAW is the simplemultiple-attribute decision-making method and is the basisof decision-making analysisThe process of SAW involves thestandardization of the decisionmatrix weight determinationand alternative ranking it is a little different from the TOPSISmethod

Firstly we standardize the decision-making matrixAccording to Zhu and Xu [35] all attribute values can betransformed into the benefit attribute

h1015840ij = hij if Oj is the benefit attribute

(hij)C if Oj is the cost attribute (30)

where (hij)C is the complement of hij as follows (hij)C =1 minus hijMeanwhile it can calculate the attributeweight120596 by using

the maximizing deviation method

120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)

Then we calculate the Euclidean distance of the decision-making matrix by using (5) as in Table 7

Finally it can rank green suppliers by

Ci = nsumj=1120596jdij (32)

where Ci represents the evaluation value of the nthsupplier

Based on calculation the evaluation values are as follows

C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209


Evaluation index system

of green supplier

Product level Service level Development levelEnvironmental

competitiveness

Quality managementsystem

Relative price level

Equipment

Product qualificationratio

Logistics cost

On-time delivery rate

Order completion rate

Services responsespeed

Service satisfaction

Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission

Cleaner productionlevel

Green enterpriseimage

Green supplier Green supplier Green supplier

(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An

Figure 2 The evaluation index system of a green supplier

Table 5 Attribute hesitancy degree of supplier

O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)


63 Results Comparison It is showed that even though thecomparison result of the three methods is that 1198602 is alwaysthe ideal supplier the new algorithm pays more attention tothe environmental index and 1198604 changes greatly It is thereason that the hesitancy degree of1198604 is higherThen a higherhesitancy degree makes distance bigger between 1198604 and thenegative ideal point In this case 1198604 in the improved type


Table 6 The improved type signed distance

O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326

Table 7 The Euclidean distance of suppliers

O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639

signed distance is closer to the ideal point So the improveddistance has a more dipartite degree

It can be found that the improved TOPSIS method issimple and highly sensitive For example we change thevalue of attribute 1198748 of supplier Α 2 that is to say ℎ28 =04 02 04 01 and it can get the changed result by usingthe improved TOPSIS and SAW method 1198601 ≻ 1198602 ≻ 1198604 ≻1198603 obviously1198601 is the ideal supplier Moreover it can get theunchanged result by the TOPSIS method 1198602 ≻ 1198601 ≻ 1198603 ≻1198604 so it has the same order as before and1198602 is still the idealsupplier Therefore the result responds to the subtle changedue to the high sensitivity of the improved TOPSIS methodOn the other hand it reflects that the improved TOPSISmethod is used widely and responds to changes sensitively

64 Algorithm Advantage By comparison the advantages ofthe algorithm are the following

(i)This paper proposes the improved type signed distancewhich adds the hesitancy degree And the new method has adipartite degree

(ii)Themethod of determining weight is the maximizingdeviation method which is more objective On the otherhand deviation of adding hesitancy degree is more reliable

(iii) The hesitancy degree pays more attention to thehesitancy level of the decision-maker and the ideal solutionmethod truthfully reflects distance So it not only affectsalternativesrsquo ranking but also affects the selection of greensuppliers

7 Conclusion

The green industry has developed into a pillar industry inthe economy development Meanwhile suppliers occupy animportant position in a supply chain particularly supplierevaluation involves the optimization problem of a green sup-ply chain Thus this paper proposes the new type algorithmsand indicators which have an important value of practicalsignificance

This paper determines the index system of a greensupplier firstly by using the DEMATEL method and thengets the decision-making matrix by a decision-maker andhesitancy degree Moreover the method of maximizingdeviation can help in obtaining attribute weight Based oncalculation it can get relative closeness Finally suppliers canbe ranked by relative closeness Subsequently a case provesthe effectiveness of the algorithm

The example proves that the improved type signed dis-tance of TOPSIS can distinguish greatly for green suppliersDue to space limitation the study only lists the limitingfactors In the future research would be devoted to algorithmimprovement and study on the influence factors

Data Availability

The data used to support the findings of this study areincluded within the article


Conflicts of Interest

There are no conflicts of interests regarding the publication ofthis manuscript

Acknowledgments

Thispaper is supported by the Liaoning Provincial FederationSocial Science Circles Department fund item ldquoResearch onefficiency measurement and promotion strategy of equip-ment manufacturing industry on the supply side reformof Liaoning provincerdquo (serial number 2019lslktjd-020) andis also supported by the Liaoning Association for Scienceand Technology think-tank item ldquoResearch on efficiencymeasurement and promotion strategy of industry on thesupply side reform of Liaoning provincerdquo (serial numberLNKX2018-2019A8)

References

[1] L XinXing and P SuHua ldquoResearch on supplier evaluation andselection based onAHPandTOPSIS in green supply chainrdquo SoScience vol 25 no 2 pp 53ndash56 2011

[2] P K Humphreys Y K Wong and F T S Chan ldquoIntegratingenvironmental criteria into the supplier selection processrdquoJournal of Materials Processing Technology vol 138 no 1-3 pp349ndash356 2003

[3] G W Dickson ldquoAn analysis of vendor selection systems anddecisionsrdquo Journal of Purchasing vol 2 no 1 pp 5ndash17 1966

[4] R Handfield S V Walton R Sroufe and S A MelnykldquoApplying environmental criteria to supplier assessment astudy in the application of the Analytical Hierarchy ProcessrdquoEuropean Journal of Operational Research vol 141 no 1 pp 70ndash87 2002

[5] K Shaw R Shankar S S Yadav and L S Thakur ldquoSupplierselection using fuzzy AHP and fuzzy multi-objective linearprogramming for developing low carbon supply chainrdquo ExpertSystems with Applications vol 39 no 9 pp 8182ndash8192 2012

[6] C-W Hsu T-C Kuo S-H Chen and A H Hu ldquoUsingDEMATEL to develop a carbonmanagement model of supplierselection in green supply chainmanagementrdquo Journal of CleanerProduction vol 56 pp 164ndash172 2013

[7] X He and J Zhang ldquoSupplier selection study under therespective of Low-Carbon supply chain a hybrid evaluationmodel based on FA-DEA-AHPrdquo Sustainability vol 10 no 2article 564 2018

[8] A Gabus and E Fontela World Problems an Invitation toFurther thought within the Framework of DEMATEL BattelleGeneva Research Center Geneva Switzerland 1972

[9] L A Zadeh ldquoFuzzy setsrdquo Information and Computation vol 8no 3 pp 338ndash353 1965

[10] M R Molaei ldquoObservational modeling of topological spacesrdquoChaos Solitons amp Fractals vol 42 no 1 pp 615ndash619 2009

[11] M R Molaei ldquoRelative semi-dynamical systemsrdquo InternationalJournal of Uncertainty Fuzziness and Knowledge-Based Systemsvol 12 no 2 pp 237ndash243 2004

[12] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 no 1 pp 87ndash96 1986

[13] V Torra andYNarukawa ldquoOn hesitant fuzzy sets and decisionrdquoin Proceedings of the IEEE International Conference on Fuzzy

Systems pp 1378ndash1382 IEEE Jeju-do Republic of KoreaAugust 2009

[14] M Xia and Z Xu ldquoHesitant fuzzy information aggregationin decision makingrdquo International Journal of ApproximateReasoning vol 52 no 3 pp 395ndash407 2011

[15] X Zhang and Z Xu ldquoHesitant fuzzy QUALIFLEX approachwith a signed distance-based comparison method for multiplecriteria decision analysisrdquo Expert Systems with Applications vol42 no 2 pp 873ndash884 2015

[16] Z S Xu and M Xia ldquoDistance and similarity measures forhesitant fuzzy setsrdquo Information Sciences vol 181 no 11 pp2128ndash2138 2011

[17] SMinghua andXQingxian ldquoGreen supplier selection decisionof hesitation fuzzy language based on prospect theory [JOL]rdquoStatistics amp Decision vol 2018 no 21 pp 46ndash50 2018

[18] JWu andQ Cao ldquoResearch on green supplier selectionmethodin uncertain decision environmentrdquo Operations Research andManagement Science vol 21 no 1 pp 220ndash225 2012

[19] C Y Ran ldquoHesitant fuzzy multi-attribute decision makingmethod based on new symbol distancerdquo Control and Decision2018

[20] S Lin X D Liu and etal ldquoUnknown hesitant fuzzy decisionmaking method based on improved symbol distancerdquo Controland Decision no 1 pp 186ndash192 2018

[21] Z Xu and X Zhang ldquoHesitant fuzzy multi-attribute decisionmaking based on TOPSIS with incomplete weight informationrdquoKnowledge-Based Systems vol 52 pp 53ndash64 2013

[22] CW Churchman R L Ackoff and E L Arnoff Introduction toOperations Research John Wiley amp Sons New York NY USA1957

[23] B Roy ldquoProblems and methods with multiple objective func-tionsrdquo Mathematical Programming vol 1 no 1 pp 239ndash2661971

[24] R Farzipoor Saen ldquoDeveloping a new data envelopment anal-ysis methodology for supplier selection in the presence ofboth undesirable outputs and imprecise datardquo13e InternationalJournal of AdvancedManufacturing Technology vol 51 no 9-12pp 1243ndash1250 2010

[25] A Azadeh and S M Alem ldquoA flexible deterministic stochasticand fuzzy Data Envelopment Analysis approach for supplychain risk and vendor selection problem simulation analysisrdquoExpert Systems with Applications vol 37 no 12 pp 7438ndash74482010

[26] T Yang and C Kuo ldquoA hierarchical AHPDEA methodologyfor the facilities layout design problemrdquo European Journal ofOperational Research vol 147 no 1 pp 128ndash136 2003

[27] D Falsini F Fondi and M M Schiraldi ldquoA logistics providerevaluation and selection methodology based on AHP DEAand linear programming integrationrdquo International Journal ofProduction Research vol 50 no 17 pp 4822ndash4829 2012

[28] S K Mangla K Govindan and S Luthra ldquoPrioritizing thebarriers to achieve sustainable consumption and productiontrends in supply chains using fuzzy Analytical Hierarchy Pro-cessrdquo Journal of Cleaner Production vol 151 pp 509ndash525 2017

[29] T L SaatyDecisionMaking with Dependence and Feedback13eAnalytic Network Process RWS Publisher 1996

[30] S Vinodh S G Gautham R Anesh Ramiya and DRajanayagam ldquoApplication of fuzzy analytic network processfor agile concept selection in a manufacturing organisationrdquoInternational Journal of Production Research vol 48 no 24 pp7243ndash7264 2010


[31] E A Bakeshlou A A Khamseh M A G Asl J Sadeghi andM Abbaszadeh ldquoEvaluating a green supplier selection problemusing a hybrid MODM algorithmrdquo Journal of Intelligent Manu-facturing vol 28 no 4 pp 913ndash927 2017

[32] C L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications vol 186 Springer Heidelberg Ger-many 1981

[33] G Buyukozkan and G Cifci ldquoA novel hybrid MCDM approachbased on fuzzy DEMATEL fuzzy ANP and fuzzy TOPSIS toevaluate green suppliersrdquo Expert Systems with Applications vol39 no 3 pp 3000ndash3011 2012

[34] A Fallahpour E Udoncy Olugu S Nurmaya Musa K YewWong and S Noori ldquoA decision support model for sustainablesupplier selection in sustainable supply chain managementrdquoComputers amp Industrial Engineering vol 105 pp 391ndash410 2017

[35] B Zhu and Z S Xu ldquoHesitant fuzzy Bonferroni means formulti-criteria decision makingrdquo Journal of the OperationalResearch Society vol 64 no 12 pp 1831ndash1840 2013

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2 Problem Description andEvaluation Process

This paper discusses the existing problems of green supplierevaluation in the multiple attributes And the hesitant fuzzyset can solve problems of the fuzzy information and theuncertain index system the DEMATEL method can deter-mine the evaluation index Based on the above methodsthe study shows the problem description and the evaluationprocess

21 Problem Description Under the background of a greensupply chain determining the alternative suppliers is neces-sary firstly Then it can determine the attribute of evaluationindex by the DEMATEL method and the structure decisionmatrix under a hesitant fuzzy set Based on the abovedescription the paper defines the symbols and interpretationas follows

Definition 1 119860 = 1198601 1198602 sdot sdot sdot 119860 119894 | 119894 = 1 2 sdot sdot sdot 119899 denotesthe set of suppliers and 119860 119894 is the 119894119905ℎ green supplier

Definition 2 119874 = 1198741 1198742 sdot sdot sdot 119874119895 | 119895 = 1 2 sdot sdot sdot 119898 denotesthe set of attributes and 119874119895 is the 119895119905ℎ attributeDefinition 3 120596 = 1205961 1205962 sdot sdot sdot 120596119895 | 119895 = 1 2 sdot sdot sdot 119898 denotesthe set of attribute weights and 120596119895 is the 119895119905ℎ attribute weightwhere 120596119895 isin [0 1] and sum119898119895=1 120596119895 = 1Definition 4 ℎ119894119895 is the hesitant fuzzy set and it representsall evaluation values in 119874119895 of 119860 119894 and this paper structuresa hesitant fuzzy set decision matrix 119867 = (ℎ119894119895)119899times119898 and ℎ119894119895 =120574120582119894119895 | 120582 = 1 2 sdot sdot sdot 119897 where 120574120582119894119895 is expert estimation

Definition 5 Δ 119894119895 is the hesitancy degree in the scheme and0 le Δ 119894119895 le 1(119894 = 1 2 sdot sdot sdot 119899 119895 = 1 2 sdot sdot sdot 119898)Definition 6 119889(1198671 1198672) represents the Euclidean distance oftwo hesitant fuzzy sets

Definition 7 119889lowast(119867119894 119867119895) represents the improvement distanceof adding hesitancy degree

Definition 8 119888(119860 119894) represents the relative closeness and 119894 =1 2 sdot sdot sdot 119899Definition 9 B = (bij)itimesj is the direct effect matrix in theDEMATELmethod in which bij represents expert evaluationand is written by a 5-degree scoring standard bij is giveninteger score of 0-4 representing ldquoNo influence(0)rdquo ldquoLowinfluence(1)rdquo ldquoGeneral influence(2)rdquo ldquoHigh influence(3)rdquoand ldquoVery high influence(4)rdquo bij represents correlationdegree from index ith to index jth And D is the standardizedmatrix of matrix B

Definition 10 T is the total effect matrix in the DEMATELmethod and T = (tij)itimesj = D(E minus D)minus1

Definition 11 fi represents effect degree and fi = sumnj=1 tij (i =1 2 sdot sdot sdot n)

Definition 12 ei represents affected degree and ei =sumnj=1 tji (i = 1 2 sdot sdot sdot n)

Definition 13 mi represents centrality degree and mi = fi +ei (i = 1 2 sdot sdot sdot n)Definition 14 ni represents cause degree and ni = fi minus ei (i =1 2 sdot sdot sdot n)22 13e Evaluation Process The purpose of this paper isthat using fuzzy language evaluates the green supplier theprocess involves method selection weight determinationand index selection In order to solve the problems this paperdetermines the evaluation index by the DEMATEL methodredefines the improved distance formula based on a hesitantfuzzy set and extends a new evaluation method Figure 1shows the system of supplier evaluation

Based on the analysis the algorithm of the evaluationsystem is summarized as follows

Step 1 Formulate appropriate green suppliers and attributesby using the DEMATEL method and denote them by 119860 =1198601 1198602 sdot sdot sdot 119860 119894 | 119894 = 1 2 sdot sdot sdot 119899 and 119874 = 1198741 1198742 sdot sdot sdot 119874119895 |119895 = 1 2 sdot sdot sdot 119898 respectivelyStep 2 Construct hesitant fuzzy decision matrix 119867 =(ℎ119894119895)119899times119898Step 3 Calculate positive ideal solution119860+ and negative idealsolution 119860minusStep 4 Solve the attribute hesitancy degree of each supplierand redefine the new distance

Step 5 Adopt the maximizing deviation method to deter-mine attribute weight 120596119895Step 6 Calculate distances between the green supplier andpositive-negative ideal solution

Step 7 Compute the relative closeness 119888(119860 119894)Step 8 Rank 119888(119860 119894)(119894 = 1 2 sdot sdot sdot 119899) and select the optimalgreen supplier

3 Construct the Evaluation Index System

In Step 1 the index system is the evaluation basis of thesupplier thus the index is very important On the other handappropriate indexes play an important role in the evaluationgreen supplier

31 Construct the Initial Index The index is the importantelement to evaluate the supplier Dickson (1996) [3] is themost influential in supplier evaluation he evaluated theevaluation indexes of 23 suppliers and indicated that the















influence matrix













D = 1max1leilensumn

j=1 bijB (1)










119867 = ⟨119909 ℎ (119909)⟩ | 119909 isin 119883 (2)


119867 =

[[[[[[[[

ℎ11 ℎ12 ℎ1119898ℎ21 ℎ22 ℎ2119898

dℎ1198991 ℎ1198992 ℎ119899119898

]]]]]]]] (3)



Δ = 1C119897

119897sum120582gt120590=1

10038161003816100381610038161003816120574120582 minus 12057412059010038161003816100381610038161003816 119894119891 119897 gt 10 119894119891 119897 = 1 (4)




119897sum119902=1

10038161003816100381610038161003816119867120582(119902)1 minus 119867120582(119902)2 100381610038161003816100381610038162 (5)











119889lowast119894119895 (120596) = 119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) 120596119895119894 = 1 2 119899 119895 = 1 2 119898

(7)



119894=1

119889lowast119894119895 (120596)

= 119899sum119894=1

119899sum119896=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus ℎ120582(119902)119896119895

1003816100381610038161003816100381610038162(1 minus Δ 119894119895) (1 minus Δ 119896119895) 119895 = 1 2 119898

(8)


max 119889lowast (120596) = 119898sum119895=1

119899sum119894=1

119899sum119896=1


119895=1

120596119895 = 1(9)


119891 (120596 120593) = 119898sum119895=1

119899sum119894=1

119899sum119896=1

120596119895119889lowast (ℎ119894119895 ℎ119896119895) + 1205932 (119898sum119895=1

120596119895 minus 1) (10)



120597119891120597120596119895 =119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) + 120593120596119895 = 0 (11)

120597119891120597120593 = 12 (119898sum119895=1

1205962119895 minus 1) = 0 (12)




120593 = minusradic 119898sum119895=1

( 119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895))2 (14)




(15)


120596119895 = 119863119895radicsum119898119895=11198632119895 119895 = 1 2 119898 120596119895 isin [0 1] (119895 = 1 2 119898)

(16)


120596lowast119895 = 120596119895radicsum119898119895=1 120596119895 119895 = 1 2 119898 (17)







119860+ = ⟨119909119895max119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)+ (ℎ21)+ (ℎ1198971)+⟩ ⟨1199092 (ℎ12)+ (ℎ22)+ (ℎ1198972)+⟩ ⟨119909119898 (ℎ1119898)+ (ℎ2119898)+ (ℎ119897119898)+⟩

(18)

119860minus = ⟨119909119895min119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898


(19)


(119889lowast119894 )+ = 119898sum119895=1

119889lowast (ℎ119894119895 ℎ+119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(20)

(119889lowast119894 )minus = 119898sum119895=1

119889lowast (ℎ119894119895 ℎminus119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(21)






























⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩





⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018






















influence matrix













D = 1max1leilensumn

j=1 bijB (1)










119867 = ⟨119909 ℎ (119909)⟩ | 119909 isin 119883 (2)


119867 =

[[[[[[[[

ℎ11 ℎ12 ℎ1119898ℎ21 ℎ22 ℎ2119898

dℎ1198991 ℎ1198992 ℎ119899119898

]]]]]]]] (3)



Δ = 1C119897

119897sum120582gt120590=1

10038161003816100381610038161003816120574120582 minus 12057412059010038161003816100381610038161003816 119894119891 119897 gt 10 119894119891 119897 = 1 (4)




119897sum119902=1

10038161003816100381610038161003816119867120582(119902)1 minus 119867120582(119902)2 100381610038161003816100381610038162 (5)











119889lowast119894119895 (120596) = 119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) 120596119895119894 = 1 2 119899 119895 = 1 2 119898

(7)



119894=1

119889lowast119894119895 (120596)

= 119899sum119894=1

119899sum119896=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus ℎ120582(119902)119896119895

1003816100381610038161003816100381610038162(1 minus Δ 119894119895) (1 minus Δ 119896119895) 119895 = 1 2 119898

(8)


max 119889lowast (120596) = 119898sum119895=1

119899sum119894=1

119899sum119896=1


119895=1

120596119895 = 1(9)


119891 (120596 120593) = 119898sum119895=1

119899sum119894=1

119899sum119896=1

120596119895119889lowast (ℎ119894119895 ℎ119896119895) + 1205932 (119898sum119895=1

120596119895 minus 1) (10)



120597119891120597120596119895 =119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) + 120593120596119895 = 0 (11)

120597119891120597120593 = 12 (119898sum119895=1

1205962119895 minus 1) = 0 (12)




120593 = minusradic 119898sum119895=1

( 119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895))2 (14)




(15)


120596119895 = 119863119895radicsum119898119895=11198632119895 119895 = 1 2 119898 120596119895 isin [0 1] (119895 = 1 2 119898)

(16)


120596lowast119895 = 120596119895radicsum119898119895=1 120596119895 119895 = 1 2 119898 (17)







119860+ = ⟨119909119895max119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)+ (ℎ21)+ (ℎ1198971)+⟩ ⟨1199092 (ℎ12)+ (ℎ22)+ (ℎ1198972)+⟩ ⟨119909119898 (ℎ1119898)+ (ℎ2119898)+ (ℎ119897119898)+⟩

(18)

119860minus = ⟨119909119895min119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898


(19)


(119889lowast119894 )+ = 119898sum119895=1

119889lowast (ℎ119894119895 ℎ+119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(20)

(119889lowast119894 )minus = 119898sum119895=1

119889lowast (ℎ119894119895 ℎminus119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(21)






























⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩





⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018














119867 = ⟨119909 ℎ (119909)⟩ | 119909 isin 119883 (2)


119867 =

[[[[[[[[

ℎ11 ℎ12 ℎ1119898ℎ21 ℎ22 ℎ2119898

dℎ1198991 ℎ1198992 ℎ119899119898

]]]]]]]] (3)



Δ = 1C119897

119897sum120582gt120590=1

10038161003816100381610038161003816120574120582 minus 12057412059010038161003816100381610038161003816 119894119891 119897 gt 10 119894119891 119897 = 1 (4)




119897sum119902=1

10038161003816100381610038161003816119867120582(119902)1 minus 119867120582(119902)2 100381610038161003816100381610038162 (5)











119889lowast119894119895 (120596) = 119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) 120596119895119894 = 1 2 119899 119895 = 1 2 119898

(7)



119894=1

119889lowast119894119895 (120596)

= 119899sum119894=1

119899sum119896=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus ℎ120582(119902)119896119895

1003816100381610038161003816100381610038162(1 minus Δ 119894119895) (1 minus Δ 119896119895) 119895 = 1 2 119898

(8)


max 119889lowast (120596) = 119898sum119895=1

119899sum119894=1

119899sum119896=1


119895=1

120596119895 = 1(9)


119891 (120596 120593) = 119898sum119895=1

119899sum119894=1

119899sum119896=1

120596119895119889lowast (ℎ119894119895 ℎ119896119895) + 1205932 (119898sum119895=1

120596119895 minus 1) (10)



120597119891120597120596119895 =119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) + 120593120596119895 = 0 (11)

120597119891120597120593 = 12 (119898sum119895=1

1205962119895 minus 1) = 0 (12)




120593 = minusradic 119898sum119895=1

( 119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895))2 (14)




(15)


120596119895 = 119863119895radicsum119898119895=11198632119895 119895 = 1 2 119898 120596119895 isin [0 1] (119895 = 1 2 119898)

(16)


120596lowast119895 = 120596119895radicsum119898119895=1 120596119895 119895 = 1 2 119898 (17)







119860+ = ⟨119909119895max119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)+ (ℎ21)+ (ℎ1198971)+⟩ ⟨1199092 (ℎ12)+ (ℎ22)+ (ℎ1198972)+⟩ ⟨119909119898 (ℎ1119898)+ (ℎ2119898)+ (ℎ119897119898)+⟩

(18)

119860minus = ⟨119909119895min119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898


(19)


(119889lowast119894 )+ = 119898sum119895=1

119889lowast (ℎ119894119895 ℎ+119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(20)

(119889lowast119894 )minus = 119898sum119895=1

119889lowast (ℎ119894119895 ℎminus119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(21)






























⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩





⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018












119889lowast119894119895 (120596) = 119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) 120596119895119894 = 1 2 119899 119895 = 1 2 119898

(7)



119894=1

119889lowast119894119895 (120596)

= 119899sum119894=1

119899sum119896=1

120596119895radic(1119897) sum119897119902=1

100381610038161003816100381610038161003816ℎ120582(119902)119894119895 minus ℎ120582(119902)119896119895

1003816100381610038161003816100381610038162(1 minus Δ 119894119895) (1 minus Δ 119896119895) 119895 = 1 2 119898

(8)


max 119889lowast (120596) = 119898sum119895=1

119899sum119894=1

119899sum119896=1


119895=1

120596119895 = 1(9)


119891 (120596 120593) = 119898sum119895=1

119899sum119894=1

119899sum119896=1

120596119895119889lowast (ℎ119894119895 ℎ119896119895) + 1205932 (119898sum119895=1

120596119895 minus 1) (10)



120597119891120597120596119895 =119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895) + 120593120596119895 = 0 (11)

120597119891120597120593 = 12 (119898sum119895=1

1205962119895 minus 1) = 0 (12)




120593 = minusradic 119898sum119895=1

( 119899sum119894=1

119899sum119896=1

119889lowast (ℎ119894119895 ℎ119896119895))2 (14)




(15)


120596119895 = 119863119895radicsum119898119895=11198632119895 119895 = 1 2 119898 120596119895 isin [0 1] (119895 = 1 2 119898)

(16)


120596lowast119895 = 120596119895radicsum119898119895=1 120596119895 119895 = 1 2 119898 (17)







119860+ = ⟨119909119895max119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)+ (ℎ21)+ (ℎ1198971)+⟩ ⟨1199092 (ℎ12)+ (ℎ22)+ (ℎ1198972)+⟩ ⟨119909119898 (ℎ1119898)+ (ℎ2119898)+ (ℎ119897119898)+⟩

(18)

119860minus = ⟨119909119895min119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898


(19)


(119889lowast119894 )+ = 119898sum119895=1

119889lowast (ℎ119894119895 ℎ+119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(20)

(119889lowast119894 )minus = 119898sum119895=1

119889lowast (ℎ119894119895 ℎminus119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(21)






























⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩





⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018












119860+ = ⟨119909119895max119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898

= ⟨1199091 (ℎ11)+ (ℎ21)+ (ℎ1198971)+⟩ ⟨1199092 (ℎ12)+ (ℎ22)+ (ℎ1198972)+⟩ ⟨119909119898 (ℎ1119898)+ (ℎ2119898)+ (ℎ119897119898)+⟩

(18)

119860minus = ⟨119909119895min119894ℎ120582(119902)119894119895 ⟩ | 119895 = 1 2 119898


(19)


(119889lowast119894 )+ = 119898sum119895=1

119889lowast (ℎ119894119895 ℎ+119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(20)

(119889lowast119894 )minus = 119898sum119895=1

119889lowast (ℎ119894119895 ℎminus119895 ) 120596119895

= 119898sum119895=1

120596119895radic(1119897) sum119897119902=1


(21)






























⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩





⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018
























⟨1199095 05 06 06 07⟩ ⟨1199096 02 08 08 05⟩ ⟨1199097 06 09 09 08⟩ ⟨1199098 05 07 06 07⟩ ⟨1199099 06 06 06 09⟩ ⟨11990910 06 06 05 04⟩ ⟨11990911 05 06 08 09⟩ ⟨11990912 06 05 05 07⟩





⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018












⟨11990913 05 06 07 09⟩ ⟨11990914 05 06 06 07⟩ ⟨11990915 05 07 06 07⟩ ⟨11990916 06 06 06 09⟩

119860minus = ⟨1199091 02 03 01 02⟩ ⟨1199092 02 02 03 02⟩ ⟨1199093 01 03 02 01⟩ ⟨1199094 04 05 01 04⟩ ⟨1199095 01 01 01 01⟩ ⟨1199096 01 04 03 02⟩ ⟨1199097 01 01 02 02⟩ ⟨1199098 03 03 01 02⟩ ⟨1199099 03 03 01 01⟩ ⟨11990910 02 02 01 02⟩

⟨11990911 02 02 03 02⟩ ⟨11990912 01 03 02 01⟩ ⟨11990913 04 05 01 04⟩ ⟨11990914 01 01 01 01⟩ ⟨11990915 03 03 01 02⟩ ⟨11990916 03 03 01 01⟩

(23)



120596= (00702 00621 00539 00725 00407 00487 00416 00894 00792 00447 00739 00651 00468 00776 00553 00783)T (24)




(25)


119888 (1198601) = 05398119888 (1198602) = 05962


119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018









119888 (1198603) = 04039119888 (1198604) = 04177

(26)





120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (27)



(28)


119888 (1198601) = 05873119888 (1198602) = 06483119888 (1198603) = 03525119888 (1198604) = 03028

(29)








120596= (00778 00600 00557 00736 00453 00491 00520 00815 00769 00494 00666 00678 00488 00691 00577 00687)T (31)






C1 = 05315C2 = 05533


Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018









Table4Th

ehesitant

fuzzydecisio

n-makingmatrix

O1

O2

O3

O4

O5

O6

O7

O8

A1

05080

705

09040

303

04050

201

06050

309

07060

303

08060

502

07060

906

08010

201

A2

09070

606

07050

303

08060

303

09070

606

05020

302

04050

604

06080

906

04050

809

A3

01060

403

04020

502

02030

602

04060

502

03020

402

03050

601

04050

604

02030

502

A4

03010

502

01030

601

04030

603

04010

506

06020

101

03020

602

05040

502

05010

401

O9

O10

O11

O12

O13

O14

O15

O16

A1

09080

605

03040

504

03060

503

01030

501

05050

204

02060

105

05030

402

03040

108

A2

02040

705

06020

104

02050

806

06050

207

04050

206

05030

401

04030

106

06040

304

A3

06030

104

02030

502

05060

402

03050

201

04060

709

01030

607

03040

207

04030

601

A4

02060

504

04020

309

05030

407

05060

105

05010

602

02040

802

04070

603

05060

209



of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018










of green supplier


competitiveness



Equipment


Logistics cost





Profit growth rate

RampD input

Corporatereputation

Financial situation

Exhaust gasemission




(6) (10)(1)

(2)(7) (10)

(4)

(5)

(3)(8)

(9)

(14)

(15)

(16)(12)

(13)

A1 Ai An



O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 01833 03167 02333 03167 025 03167 01667 036671198602 01667 02333 03000 01667 01667 01167 01833 030001198603 02667 01833 02167 02167 01167 02833 01167 016671198604 02167 02833 01667 02667 02667 02167 01667 02500O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 02333 01000 01833 02333 01667 03000 01667 036671198602 02667 02833 03167 02667 02167 02167 02667 015001198603 02667 01667 02167 02167 02667 03333 02667 026671198604 02833 02167 03667 02167 02500 03000 02333 03667

C3 = 04755C4 = 05132

(33)





O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018










O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 14348 16376 12367 17734 12612 15341 09454 234521198602 17654 12589 16130 16354 07189 09087 10320 293011198603 16868 12014 12638 17710 09284 10717 08589 167611198604 18422 18601 10545 17748 09914 11574 11494 16274O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 22699 07393 13220 17144 08998 20262 12613 183291198602 15705 15438 17981 16100 08564 15685 12320 140201198603 20515 09487 16218 14917 17668 20106 12394 234451198604 17027 10518 23468 14318 09706 18417 15723 19326


O1 1198742 1198743 1198744 1198745 1198746 1198747 11987481198601 07274 05361 04212 05326 06673 05507 05954 074721198602 08744 04244 05472 07771 03436 04894 06404 113861198603 07344 04444 03669 05104 04059 04387 05959 062721198604 08674 04924 03505 05677 04823 05302 07634 06444O9 11987410 11987411 11987412 11987413 11987414 11987415 119874161198601 09364 03591 03947 05530 04012 01573 03288 040811198602 04416 03591 04306 06003 03498 02850 02995 045551198603 05036 03591 03590 04898 07335 02532 02932 040551198604 04645 03591 04817 05157 03971 01573 04387 05639







7 Conclusion




Data Availability





Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018











Acknowledgments


References













































Journal of












Journal of







Volume 2018






Volume 2018





















Journal of












Journal of







Volume 2018






Volume 2018








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