A dynamic generalized fuzzy multi-criteria croup decision making approach for green supplier segmentation

Supplier selection and segmentation are crucial tasks of companies in order to reduce costs and increase the competitiveness of their goods. To handle uncertainty and dynamicity in the supplier segmentation problem, this research thus proposes a new dynamic generalized fuzzy multi-criteria group decision making (MCGDM) approach from the aspects of capability and willingness and with respect to environmental issues. The proposed approach defines the aggregated ratings of alternatives, the aggregated weights of criteria, and the weighted ratings by using generalized fuzzy numbers with the effect of time weight. Next, we determine the ranking order of alternatives via a popular centroid-index ranking approach. Finally, two case studies demonstrate the efficiency of the proposed dynamic approach. The applications show that the proposed appoach is effective in solving the MCGDM in vague environment.

2.Tables 6a -6e are a bit confusing within the manuscript, maybe including these tables in an annex will be more convenient. 3.There must be a discussion section after the section "Comparison of the proposed method with another fuzzy MCDM method" and the conclusion section. The results are not discussed clearly for the reader. The results need to be interpreted from mathematical and operational point of view, as a reader I am afraid I need more explanation for the numbers. It looked in some places that you jumped from section to another without explaining the results. Moreover, you need to discuss the strengths of your approach, how it tackled current existing problem, and why do you think it should be considered by others. For example, have you considered a simulation study and compare the results with other methods to assess the consistency of the results?! or have you considered comparing this method with more statistically based approaches such as Multidimensional Latent Class Item Response Theory Models?! There should be more discussion before you present your conclusion. Responses: 1.Thank you very much for your comments. The authors have added some sentences in the introduction and literature review section to discuss more about the shortcomings of the existing approaches and the advantages of our approach. 2.Thanks for your suggestion. The authors have moved Tables 6a -6e to appendix section. 3.Thanks for your comments. The authors have added some paragraphs to discuss about the results of the study and the advantages of our approach. Some sentences have been added in the implementation section to explain more about the calculation process. In this study, a new dynamic generalized fuzzy MCDM approach has been proposed. Then, we have compared the proposed method with another fuzzy MCDM method to show its advantages. The comparison between our proposed approach with more statistically based approaches such as Multidimensional Latent Class Item Response Theory Models should be our further research. Referee 2's Comments: While new methods for "green" supplier segmentation is certainly important, interesting, and relevant, there are several issues in this paper. 1.The methods in this paper appear to be sound, it is very hard to read and comprehend. The organization and visualization of data/results is overall, poor. 2.Background on fuzzy numbers is lengthy and a bit hard to follow. 3.There is an excess of tables, which is incredibly overwhelming and unhelpful given the complexity of the topic and notation. The tables in the literature review section are redundant or unnecessary. If tables really are necessary, for this many tables, they belong in an appendix. 4.Some terms or abbreviations are not explained and confusing. For example, in Table  6a, I'm assuming "fa" = "fair", "Ve_go" = "Very good"? This needs to be standardized and presented in a more meaningful, insightful, and visually interesting manner. For example, map responses to numbers rather than letter abbreviations, and plot a heat map of responses, rather than use a table. This can be done with ALL of the tables in this section. 5. Table 8 may be better off as some sort of visual representation (chart) rather than a table. 6.There are grammatical mistakes throughout the paper Responses: 1.Thank you very much for your comments. The authors have added some sentences in the implementation section to explain more about the data and results of this study. The authors have also moved the Tables 6a -6e to the appendix. 2.Thanks for your suggestion. The authors have moved the background on fuzzy numbers to appendix. 3.Thanks for your suggestion. The authors have moved Tables 1-3 to the appendix. 4.Thanks for your suggestion. The authors have tried to change the abbreviations of linguistic variables (Appendix B - Table 2 and other tables). 5.Thanks for your suggestion. The authors have modified the Table 8 to make it more visually. 6.The authors have tried to fix the grammatical mistakes throughout the paper.   Yes -all data are fully available without restriction

Introduction
Supplier segmentation is a step that follows supplier selection and plays an important role in organizations for reducing production costs and optimally utilizing resources. Enterprises classify their suppliers from a selected set into distinct groups with 2 different needs, characteristics, and requirements in order to adopt an appropriate strategic approach for handling different supplier segments [1]. Supplier segmentation is a highly complex decision-making problem that must consider many potential criteria and decision makers under a vague environment [2,3]. Consequently, supplier segmentation can be viewed as a fuzzy multi-criteria group decision making (MCGDM) problem.
Numerous studies in the literature have proposed fuzzy multi-criteria decision making (MCDM) approaches to select and evaluate (green/sustainable) suppliers, with some recent applications found in [4][5][6][7][8][9][10]. While several studies used multi-criteria methods and fuzzy logic systems for solving supplier segmentation problem [2,3,[11][12][13], existing studies on segmenting suppliers have paid limited attention to environmentally and socially related criteria [11]. Additionally, few studies have applied generalized fuzzy numbers (GFNs) to select or segment suppliers. Furthermore, they all have converted GFNs into normal fuzzy numbers through a normalization process and then applied fuzzy MCDM methods for normal fuzzy numbers. Nevertheless, the normalization process has a serious disadvantage -that is, the loss of information [14].
Chen [15] indicated in many practical situations that it is not possible to restrict the membership function to the normal form. Furthermore, the existing studies targeting supplier selection and segmentation only address static evaluation information for a certain period. However, in many real-life problems the decision makers are generally provided the information over different periods [16,17]. Lee et al. [16] proposed a dynamic fuzzy MCGDM method for performance evaluation, while Mehdi et al. [17] presented a new fuzzy dynamic MCGDM approach to assess a subcontractor. Overall, it seems that no study has yet to propose a dynamic MCGDM using GFNs for solving the green supplier segmentation (GSS) problem with the effect of a time weight. 3 This study primarily proposes a new dynamic generalized fuzzy MCGDM approach from the aspects of capability and willingness with respect to environmental issues. The proposed approach defines the aggregated ratings of alternatives, the aggregated weights of criteria, and the aggregated weighted ratings using GFNs with the effect of time weight. We then determine the ranking order of alternatives via a popular centroid-index ranking approach proposed by [18]. Finally, two case studies demonstrate the efficiency of the proposed approach.

Literature review on methods and criteria for supplier segmentation
This section presents an overview of the methods and criteria that have been used for supplier segmentation in the existing literature.
Kraljic [20] presented a comprehensive portfolio approach to purchasing and supply segmentation. To classify materials or components, Kraljic [20] utilized two variables, the profit impact of a given item and the supply risk, under high and low levels that yield four segments: (1) non-critical items (supply risk: low; profit impact: low), (2) leverage items, (supply risk: low; profit impact: high), (3) bottleneck items (supply risk: high; profit impact: low), and (4) strategic items (supply risk: high; profit impact: high). Dyer et al. [30] developed strategic supplier segmentation based on the differences between outsourcing strategies. According to them, firms should maintain high levels of communication with suppliers that provide strategic inputs that contribute to the 4 differential advantage of the buyer's final product. On the other hand, firms do not need to allocate significant resources to manage and work with suppliers that provide non-strategic inputs. Kaufman et al. [26] developed a strategic supplier typology that explains the differences in the composition and performance of various types of suppliers, using technology and collaboration to segment suppliers.
Svensson [27] applied three principal components, including the source of disturbance, the category of disturbance, and the type of logistics flow, in supplier segmentation. Hallikas et al. [24] described supplier and buyer dependency risks as the variables for classifying supplier relationships. Day et al. [28] presented the taxonomy of segmentation bases in which the buyer assesses the supply base from a purchasing perspective. Che [22] proposed two optimization mathematical models for the clustering and selection of suppliers. Model 1 is based on customer demands to cluster suppliers under a minimal total within cluster variation. Model 2 takes the results of Model 1 to determine the optimal supplier combination based on quantity discount and customer demands. Rezaei & Ortt [31] proposed a framework for classifying suppliers based on supplier capabilities and willingness. Using their framework, it is possible to segment suppliers using multiple criteria, but most existing methods are based on just two criteria.
Rezaei et al. [32] presented an approach for segmenting and developing suppliers using capabilities and willingness criteria. They employed the best worst method (BWM) to define the relative weight of the criteria and further applied a scatter plot to segment the suppliers, where the horizontal and vertical axes are capabilities and willingness, respectively. Segura & Maroto [21] utilized a hybrid MCDM approach based on PROMETHEE and Multi-Attribute Utility Theory and used Analytic Hierarchy Process (AHP) for eliciting the weights of the criteria. The authors further took historical and reliable indicators to classify suppliers. Bai et al. [11] presented a novel methodology 5 based on the rough set theory, VIKOR, and fuzzy C-means for green supplier segmentation, employing the dimensions of willingness and capabilities in their approach.
Aineth & Ravindran [8] proposed a quantitative framework for sustainable procurement using the criteria of economic, environmental, and social hazards. Rezaei & Lajimi [33] combined purchasing portfolio matrix, supplier potential matrix, and BWM to segment suppliers. Appendix A compares the existing methods for supplier segmentation.
Supplier segmentation is a MCGDM problem that includes many criteria and decision makers within a vague environment. However, only a few studies in the literature applied the multi-criteria method and fuzzy logic systems to segment suppliers.
Additionally, previous studies were limited to using normal fuzzy numbers and addressing the static evaluation information at a certain period to segment suppliers. Rezaei & Ortt [2] utilized the fuzzy AHP approach to segment suppliers using their capabilities and willingness criteria. Haghighi & Salahi [13] used the integrated fuzzy AHP approach and c-means algorithm to cluster suppliers. Akman [34] proposed a hybrid approach, including VIKOR, confirmatory factor analysis, and fuzzy c-means, to evaluate and segment suppliers in an automobile manufacturing company. The criteria of suppliers' capability and willingness were used to cluster suppliers. Lo & Sudjatmika [12] presented a modified fuzzy AHP approach for evaluating suppliers using bell-shaped membership functions. To our knowledge, no prior studies have developed the dynamic generalized fuzzy MCGDM approach with respect to environmental issues for solving supplier segmentation problem.

Green supplier segmentation criteria
Identifying the GSS criteria is one of the main challenges of a business enterprise to formulate proper supplier segmentation. To conduct GSS, several economic, environmental, and social dimensions should be considered [6], yet the majority of prior research only considered the evaluation criteria from the economic aspect. To segment the Use plain style 6 suppliers, our study's proposed approach takes into account not only economic criteria, but also environmental and social criteria. Appendix A summarizes the capabilities and willingness criteria drawing the greatest attention in recent literature.

Establishment of a new approach for solving green supplier selection and segmentation
This section develops a new generalized fuzzy dynamic MCGDM approach to solve the green supplier selection and segmentation problem. The procedure of the proposed approach is described as follows. A dynamic MCGDM approach can be concisely expressed in matrix format as:

Identifying the green capabilities and willingness criteria
Aggregating the importance weights of the criteria  can be evaluated as:

Constructing the weighted fuzzy decision matrix
The weighted decision matrices 1

Defuzzification
This study applies the popular centroid-index ranking approach proposed by [18] to determine the ranking order of alternatives.

Implementation of the proposed dynamic generalized fuzzy MCGDM approach
This section applies the proposed approach in the case of a medium-sized transport equipment company located in northern Vietnam. The managers of this company have become perplexed on how to effectively manage their suppliers to maximize their profit due to the increase in the number of suppliers. We apply the proposed approach to the process of this firm's green supplier segmentation to help it segment its suppliers and test the efficacy of the proposed method. Data were collected by conducting semi-structured What was your justification to divide the suppliers?? support with evidence 9 interviews with the company's top managers and department heads (decision-makers).
Three decision makers (D1, D2, and D3) were requested to separately evaluate the importance weights of the capabilities and willingness criteria and the ratings of GSS at three different times (t1, t2, and t3). We characterize the entire GSS procedure by the following steps.
Step 1: Aggregate the importance weights of the respective capabilities and willingness criteria.
Step 2: Aggregate the ratings of green suppliers versus capabilities and willingness criteria, respectively.
Step 3: Construct the weighted fuzzy decision matrices.
Step 4: Calculation of the distance of each green supplier.
Step 5: Segment the green suppliers.
Steps 1 and 2 were performed by the company's managers (i.e., the three decisionmakers D1, D2, and D3) without any intervention from the authors. Steps 3 to 5 were calculated using the proposed approach.

Aggregation of the importance weights of the respective green capabilities and willingness criteria
Following the review of the literature and discussions with the top managers and department heads, we select six capabilities (i.e., price/cost -C1, delivery -C2, quality -C3, reputation and position in industry -C4, financial position -C5, hazardous waste management -C6) and four willingness criteria (i.e., commitment to quality -W1, commitment to continuous improvement in product and process -W2, relationship closeness -W3, willingness to share information, ideas, technology, and cost savings -W4) for evaluating and segmenting suppliers. After determining the green suppliers' criteria, the three company's managers are asked to define the level of importance of each criterion through a linguistic variable. Table 1 shows the aggregate weights of the criteria using Eq. (1).

Aggregation of the ratings of green suppliers versus the capabilities and willingness criteria
The decision makers define the suitability ratings of twelve green suppliers (i.e., 1 12 ,..., AA ) versus the capabilities and willingness criteria using the linguistic variables.
Tables 3a to 3e (in Appendix C) present the aggregated suitability ratings of the suppliers versus the six capabilities criteria (i.e., 17 ,..., CC ) and four willingness criteria (i.e., 16 ,..., ) WW from the three decision makers obtained from Eq. (2) and  Table 4 shows the final fuzzy evaluation values of each green supplier using Eqs.

Calculation of the distance of each green supplier
We obtain the distance between the centroid point and the minimum point Go = (0,124, 0,600) of each green supplier as depicted in Table 5 by using the data in Table 4 and the ranking approach proposed by [18].

Segmentation of the suppliers
Based on the distance scores for the capabilities and willingness of each green supplier, we assign 12 green suppliers to one of four segments ( Fig. 1) using Step 6 of the proposed methodology. In this step, the cut-off points of the green supplier's capabilities 12 and willingness are 0.2084 and 0.1814, respectively. Figure 1 and Table 6 show that one green supplier is assigned to Group 1, three green suppliers to Group 2, one green supplier to Group 3, and seven green suppliers to Group 4. Thus, the company has seven good green suppliers, but five of them lack capabilities, willingness, or both.
The results indicate that the company can use different strategies to handle various segments and may try and develop those green suppliers that are less capable and less willing to cooperate (i.e., Group 1 green suppliers) or terminate its relationship with them in favor of good alternatives [2,3]. Group 2 green suppliers are willing to cooperate, but are less competent to meet the buyer's requirements. The company should help these green suppliers improve their capabilities and performance or replace them with capable ones in the short term [35]. Group 3 green suppliers have high capabilities, but exhibit a low-level willingness to cooperate. The company should focus on improving its relationship with these green suppliers and determine various approaches on how to become attractive to them [36]. Group 4 green suppliers, which are the best green suppliers of the company, have great capabilities and a high level of willingness. The company should maintain a close long-term relationship with these green suppliers [31].

MCDM method
This section compares the proposed approach in time ,1 u tu  with another fuzzy MCDM approach to demonstrate its advantages and applicability by reconsidering the example investigated by [2]. In this example, a medium-sized broiler (meat-type chicken) company in the food industry intends to segment its suppliers. Six criteria for capabilities and six criteria for willingness are selected to segment 43 suppliers based on the decision makers (i.e., the managers). Table 7 shows the importance weights of the capabilities and willingness criteria.   Table 8 demonstrates the averaged ratings of suppliers versus the capabilities and willingness criteria based on the data presented in Table 5 in the work of [2] and in Table 2 of this paper. We obtain the distance between the centroid and minimum points of 43 suppliers by using the ranking approach proposed by [17] as denoted in Table 9.  Table 10 shows that three suppliers are assigned to Group 1, nine suppliers to Group 2, three suppliers to Group 3, and twenty-eight suppliers to Group 4.

Discussions and Conclusions
Green supplier segmentation (GSS) is a critical marketing activity for companies having many suppliers. Rather than formulating individual strategies for each supplier, companies can now adopt an appropriate strategic approach for handling different supplier segments. To manage the uncertainty and dynamics of GSS, this study develops a new dynamic generalized fuzzy MCGDM using capabilities and willingness criteria. The proposed approach contributes to the body of GSS literature in four significant directions.
First, it expands previous studies by using GFNs instead of fuzzy numbers. Second, it is able to solve the supplier segmentation problem at different periods instead of one period.
It should be supported by literature 18 Third, it considers not only economic criteria, but also environmental and social criteria from the aspects of suppliers' capability and willingness. Fourth, the approach can solve the GSS problem and also be employed in other management problems under similar settings.
The proposed framework uses GFNs to express the aggregated ratings of alternatives, the aggregated importance weights of criteria, and the aggregated weighted ratings with the effect of time weight. In order to rank the alternatives, we apply the most popular centroid-index ranking approach. We test the proposed approach by segmenting the suppliers of a medium-sized transport equipment company to illustrate its applicability.
The company can thus formulate different strategies to handle various segments based on the outcomes obtained using the proposed method. We identify at least four major green supplier strategies: (i) maintain close long-term relationships with suppliers that have strong capabilities and high willingness; (ii) improve and attract relationships with suppliers that have high capabilities, but a low-level willingness to cooperate; (iii) help suppliers that have low capabilities, but are very willing "to green" their products and processes; (iv) terminate relationships with suppliers that are less capable and less willing to cooperate. We further compare the proposed approach with another fuzzy MCDM approach to demonstrate its superiority. Findings show that the proposed approach is an effective tool for practitioners to solve GSS problems.
The study does have some limitations. First, the proposed approach does not consider the correlation of attributes. Therefore, it is difficult to derive the weights of the decision criteria while maintaining judgment consistency. Second, by using fuzzy sets, the proposed approach cannot handle MCGDM problems that have indeterminate and inconsistent information. Future work plans are to integrate an AHP method in MCGDM 19 by defining the importance weights of criteria. Neutrosophic sets and their extension will also be applied to express the vague information in MCGDM. 21 [20] Kraljic P. Purchasing must become supply management.

Introduction
Supplier segmentation i, which is a step that follows supplier selection and, plays an important role infor organizations forto reducinge production costs and optimally Revised Manuscript with Track Changes 2 utilizinge resources. The organizationsEnterprises classify its their suppliers from a selected set into distinct groups with different needs, characteristics, and requirements in order to adopt the an appropriate strategic approach for handling different supplier segments [1]. Supplier segmentation is a highly complex decision-making problem that must, which should consider many potential criteria and decision makers under a vague environment [2,3]. Consequently, supplier segmentation can be viewed as a fuzzy multicriteria group decision making (MCGDM) problem.
Numerous studies in the literature have proposed the fuzzy multi-criteria decision making (MCDM) approaches to select and evaluate (green/sustainable) suppliers, with s.
Additionally, few of studies have applied the generalized fuzzy numbers (GFNs) to select or segment the suppliers. Furthermore, they all of these studies have converted the GFNs into normal fuzzy numbers through a normalization process and then appliedy the fuzzy MCDM methods for normal fuzzy numbers. Nevertheless, the normalization process has a serious disadvantage -, that is, the loss of information [14].
Chen [15] indicated that in many practical situations that it is not possible to restrict the membership function to the normal form. Furthermore, the existing studies targetingfor supplier selection and segmentation only address static evaluation information forat a certain period. However, in many real-life problems, the decision makers are generally provided the information at theover different periods [16,17]. Lee et al. [16] proposed a dynamic fuzzy MCGDM method for performance evaluation, while. Mehdi et al. [17] presented a new fuzzy dynamic MCGDM approach to assess a subcontractor. Overall, iIt 3 seems that no study has yet to propose aies have proposed a dynamic MCGDM using the GFNs for solving the green supplier segmentation (GSS) problem with the effect of a time weight.
This study primarily aims to proposes a new dynamic generalized fuzzy MCGDM approach from the aspects of capability and willingness, with respect to environmental issues. The proposed approach defines the aggregated ratings of alternatives, the aggregated weights of criteria, and the aggregated weighted ratings using GFNs with the effect of time weight. We then determineThen, the ranking order of alternatives is determinedvia using a popular centroid-index ranking approach proposed by [18]. Finally, two case studies were used to demonstrate the efficiency of the proposed approach.

Literature review on methods and criteria for supplier segmentation
This section presents an overview of the methods and criteria which tahat have been used for supplier segmentation in the existing literature.
Kraljic [20] presented a comprehensive portfolio approach to purchasing and supply segmentation. To classify the materials or components, Kraljic [20] utilizedused two variables, the namely, profit impact of a given item and the supply risk, with under high and low levels that yield four segments: (1) non-critical items (supply risk: low; profit impact: low), (2) leverage items, (supply risk: low; profit impact: high), (3) bottleneck 4 items (supply risk: high; profit impact: low), and (4) strategic items (supply risk: high; profit impact: high). Dyer et al. [30] developed a strategic supplier segmentation based on the differences between outsourcing strategies. According to them authors, firms should maintain high levels of communication with suppliers that provide strategic inputs that contribute to the differential advantage of the buyer's final product. On the other hand, firms do not need to allocate significant resources to manage and work with suppliers that provide non-strategic inputs. Kaufman et al. [26] developed a strategic supplier typology that explains the differences in the composition and performance of various types of suppliers, using t. Technology and collaboration were used to segment suppliers.
Svensson [27] applied three principal components, including the source of disturbance, the category of disturbance, and the type of logistics flow, in supplier segmentation. Hallikas et al. [24] described supplier and buyer dependency risks as the variables for classifying supplier relationships. Day et al. [28] presented the taxonomy of segmentation bases in which the buyer assesses the supply base from a purchasing perspective. Che [22] proposed two optimization mathematical models for the clustering and selection of suppliers. Model 1 iwas based on customer demands to cluster suppliers with under a minimal total within cluster variation. Model 2 takesused the results of Model 1 to determine the optimal supplier combination based on quantity discount and customer demands. Rezaei & Ortt [31] proposed a framework for classifying the suppliers based on supplier capabilities and willingness. Using their framework, it is possible to segment suppliers using multiple criteria, while most thebut most existing methods are based on just two criteria.
Rezaei et al. [32] presented an approach for segmenting and developing suppliers using capabilities and willingness criteria. They employed the bBest worst method (BWM) was employed to define the relative weight of the criteria and further applied a. A scatter Additionally, previous studies were limited to use usingthe normal fuzzy numbers and addressing the static evaluation information at a certain period to segment suppliers.
Rezaei & Ortt [2] applied utilized the fuzzy AHP approach to segment suppliers using the suppliers'their capabilities and the willingness criteria. Haghighi & Salahi [13] used the integrated fuzzy AHP approach and c-means algorithm to cluster suppliers. Akman [34] proposed a hybrid approach, including VIKOR, confirmatory factor analysis, and fuzzy cmeans, to evaluate and segment suppliers in an automobile manufacturing company. The criteria of suppliers' capability and willingness were used to cluster suppliers. Lo & Sudjatmika [12] presented a modified fuzzy AHP approach for evaluating suppliers using bell-shaped membership functions. To our knowledge, no prior studies have developed the 6 dynamic generalized fuzzy MCGDM approach with respect to environmental issues for solving supplier segmentation problem.

Green supplier segmentation criteria
Identifyingication of the GSS criteria is one of the main challenges of a business enterprise to formulate the proper supplier segmentation. In To conducting the GSS, several economic, environmental, and social dimensions should be considered [6], yet.
However, the majority of prior research has only considered the evaluation criteria from thein economic aspect. To segment the suppliers, oIn thisur study's, the proposed approach takes into account not only economic criteria, but also environmental and social criteria to segment the suppliers. Appendix A summarizes tThe capabilities and willingness criteria drawing the greatest attention in recent literature. were summarized in the Appendix A

Establishment of a new approach for solving green supplier selection and segmentation
This section develops a new generalized fuzzy dynamic MCGDM approach to solve the green supplier selection and segmentation problem. The procedure of the proposed approach is described as the followsing:. A dynamic MCGDM approach can be concisely expressed in matrix format as:

Identifying the green capabilities and willingness criteria
Aggregating the importance weights of the criteria

Constructing the weighted fuzzy decision matrix
The weighted decision matricxes 1

Defuzzification
This study applies the popular centroid-index ranking approach proposed by [18] to determine the ranking order of alternatives.

Implementation of the proposed dynamic generalized fuzzy MCGDM approach
This section applies the proposed approach in the case of a medium-sized transport equipment joint stock company located in northern Vietnam. The managers of this company have become confusedperplexed on how to effectively manage their suppliers to maximize their profit due to because of the increase in the number of suppliers. We apply tThe proposed approach was applied to the process of this firm's green supplier segmentation of this company to help it segment their its suppliers and test the efficacy of 10 the proposed method. Data were collected by conducting semi-structured interviews with the company's top managers and department heads (decision-makers). Three decision makers (, i.e. D1, D2, and D3,) were requested to separately evaluate the importance weights of the capabilities and willingness criteria and the ratings of GSS at three different times (t1, t2, and t3). We characterize tThe entire GSS procedure was characterized by the following steps.: Step 1: Aggregate the importance weights of the respective capabilities and willingness criteria.
Step 2: Aggregate the ratings of green suppliers versus capabilities and willingness criteria, respectively.
Step 3: Construct the weighted fuzzy decision matrices.
Step 4: Calculation of the distance of each green supplierDefuzzify.
Step 5: Segment the green suppliers.
Steps 1 and 2 were performed by the company's managers (i.e., the three decisionmakers: D1, D2, and D3) without any intervention from the authors. Steps 3 to 5 were calculated using the proposed approach.

Aggregation of the importance weights of the respective green capabilities and willingness criteria
Following the review of the literature and discussions with the top managers and department heads, we select six capabilities (i.e., price/cost -C1, delivery -C2, quality -C3, reputation and position in industry -C4, financial position -C5, hazardous waste management -C6) and four willingness criteria (i.e., commitment to quality -W1, commitment to continuous improvement in product and process -W2, relationship closeness -W3, willingness to share information, ideas, technology, and cost savings -W4) 11 for were selected in order to evaluatinge and segmenting suppliers. After determining the green suppliers' criteria, the three company's managers are asked to define the level of importance of each criterion through a linguistic variable. Table 1 shows the aggregate weights of the criteria using Eq. (1).

Aggregation of the ratings of green suppliers versus the capabilities and willingness criteria
The decision makers define the suitability ratings of twelve green suppliers (i.e., 1 12 ,..., A A ) versus the capabilities and willingness criteria using the linguistic variables.
Tables 3a to 3e (in Appendix C) present the aggregated suitability ratings of the suppliers versus the six capabilities criteria (i.e., 1 7 ,..., C C ) and four willingness criteria (i.e., 1 6 ,..., ) W W from the three decision makers obtained from Eq. (2) and  Table 4 shows the final fuzzy evaluation values of each green supplier using Eqs.

Calculation of the distance of each green supplier
We obtain tThe distance between the centroid point and the minimum point Go = (0,124, 0,600) of each green supplier is obtained as depicted in Table 5 by using the data in Table 4 and the ranking approach proposed by [18].

Segmentation of the suppliers
Based on the distance scores for the capabilities and willingness of each green supplier, we assign 12 green suppliers are assigned to one of four segments (Fig. 1) using Step 6 of the proposed methodology. In this step, the cut-off points of the green supplier's  Figure. 1 and Table 6 show that one green supplier is assigned to Group 1, three green suppliers are assigned to Group 2, one green supplier is assigned to Group 3, and seven green suppliers are assigned to Group 4. Thus, the company has seven good green suppliers, but five of them lack in capabilities, willingness, or both.
The results indicate that the company can use different strategies to handle various segments and . The company may try and develop those the green suppliers that are less capable and less willing to cooperate (i.e., Group 1 green suppliers) or may terminate its relationship with them in favor of good alternatives [2,3]. Group 2 green suppliers are willing to cooperate, but are less competent to meet the buyer's requirements. The company should help these green suppliers improve their capabilities and performance or replace them with capable ones in the short term [35]. Group 3 green suppliers have high capabilities, but exhibithave a low-level willingness to cooperate. The company should focus on improving its relationship with these green suppliers and determine various approaches on how to become attractive to them [36]. Group 4 green suppliers, which are the best green suppliers of the company, have great capabilities and a high level of willingness. The company should maintain a close long-term relationship with these green suppliers [31].

MCDM method
This section compares the proposed approach in time , 1 u tu  with another fuzzy MCDM approach to demonstrate its advantages and applicability by reconsidering the example investigated by [2]. In this example, a medium-sized broiler (meat-type chicken) company in the food industry intends to segment their its suppliers. Six criteria for capabilities and six criteria for willingness are selected to segment 43 suppliers based on the decision makers (i.e., the managers). Table 7 shows the importance weights of the capabilities and willingness criteria.   Table 8 demonstrates the averaged ratings of suppliers versus the capabilities and willingness criteria based on the data presented in Table 5 in the work of [2] and ion Table   2 ofin this paper. We obtain tThe distance between the centroid and minimum points of 43 suppliers by is obtained using the ranking approach proposed by [17] as denoted in Table 9.

Discussions and Conclusions
Green supplier segmentation (The GSS)  In tThe proposed framework usesapproach, the GFNs were used to express the aggregated ratings of alternatives, the aggregated importance weights of criteria, and the aggregated weighted ratings with the effect of time weight. In order to rank the alternatives, we apply the most popular centroid-index ranking approach was applied. We test tThe proposed approach was applied toby segmenting the suppliers of a medium-sized transport equipment joint stock company to illustrate its applicability. The company can thus formulate different strategies to handle various segments based on the outcomes obtained using the proposed method. We identify aAt least four major green supplier strategies identified include: (i) maintaining a close long-term relationships with suppliers who that have strong capabilities and high willingness; (ii) improveing and attracting the relationships with suppliers who that have high capabilities, but have a low-level willingness to cooperate; (iii) helping suppliers who that have low capabilities, but are very willing "to green" their products and processes; (iv) terminateing the relationships with suppliers who that are less capable and less willing to cooperate. We further compare tThe proposed approach was further compared with another fuzzy MCDM approach to demonstrate its superiority. Findings showIt has been demonstrated that the proposed approach is an effective tool for practitioners to solve GSS problems.