1.INTRODUCTION
In comparison to the past, organizations today are challenging with a competitive environment, such as how products are designed, manufactured, and distributed to improve the production efficiency and reduce the total cost and finally meet the customer needs (Pan and Nagi, 2013). In fact, competitiveness has traditionally is associated with those supply chains that provide and manufacture innovative products, such as hightech products which compatible with a high degree of market instability, uncertainty in demand, and unpredictability in supply. To do so, the supply chain is needed to be fast and has a high level of maneuverability, which response to various demands and environments’ changes. Moreover, the earth’s resources are limited and continuously depleting due to large scale industrialization and globalization so that the most governments consider the alternates, as well as the judicious use of these resources (Roscoe et al., 2016). These concerns and awareness have led the organizations to attempt in achieving environmentally friendly manufacturing processes and products (Arimura et al., 2011). Green Supply Chain Management is defined as ‘‘applying integrated environmental activities related to manufacturing, supplier relations, distribution of the final product, product life cycle and all parts of the supply chain management” (Srivastava, 2007). Due to the studies, the green supplier is placed as critical part of the entire green supply chain; it acts on the cost savings and environmental protection. It can effectively improve the compatibility of the supply chain and the environment performance (Blome et al., 2014). Besides that the green supplier is strategically essential as it can determine the organization’s success in attaining green practices, an agile one can make competitive advantages for the organization in such a competitive environment with market uncertainty (Pan and Nagi, 2013). This study aims to construct a framework to select a supplier based on environmental and performance indicators on the consistency rate of suppliers into theses two dimensions.
According to the studies, proper selection of a supplier is specified the short or long term success of the organization (Büyüközkan and Arsenyan, 2009). The supplier selection problem presents which alternatives should be selected for the organization to achieve its goals. This kind of problems is mentioned as a complex multicriteria decision making (MCDM) (Liao and Rittscher, 2007) which its complexity derives from factors that may not have consistency with each other (Kilic, 2013). Actually, in today’s global competition, customer expectations have not limited to certain factors such as lower price and best quality; as they also involve production approach, warranties, social issues and many other criteria that make the supplier selection complex problem (Hamdan and Cheaitou, 2017). Also by increasing environmental concerns, green supply chain factors are proposed as a competitive advantage for the supplier. In this regard, supplier selection problem can be mentioned as a multiple criteria group decisionmaking problem that involves many conflicting evaluation criteria, including performance indicator and green factors (Qin et al., 2017). Specifically, regarding environmental factors in supplier selection can refer to the Hsu and Hu (2009) studies that suggested hazardous substance management to reduce degradation of the environment in their supplier selection process. Lee et al. (2009) suggested a model that evaluates the performance of green suppliers. Büyüközkan and Çifçi (2011) proposed a decisionmaking model for an effective, sustainable supplier evaluation based upon performance capability and environmental factors. Shen et al. (2013) rated green suppliers on their environmental performance. Rostamzadeh et al. (2015) applied fuzzy Vikor to evaluation green supply chain management. Akman (2015) proposed green supplier assessment framework on performance and green criteria. Further, Mahdiloo et al. (2015) proposed a model to evaluate practical and environmental criteria with ecoefficiency of altarnatives (suppliers). Table 1 summarized few important studies of supplier selection by considering the issues addressed, and techniques are used:
1.1.Research Gap
Most of the studies have employed in this area are focused mainly on ranking alternatives using various methods, while analysis of the supplier’s desirability in each of the environmental and performance indicators and their deviation from a total function, is the most factor in the selecting of precise and accurate green suppliers, which is not sufficient studied. Further, the rising trend for integrated approaches has been noted in recent years, thus, in this study to robust the green supplier selection framework, an integrated method is presented that included interpretive structural modeling, Fuzzy MICMAC analysis, FAHP and Fuzzy Vikor to consider uncertain and various circumstances based on the inaccuracy and unknown principle of human judgment.
2.GREEN SUPPLY CHAIN MANAGEMENT
Green supply chain management aims to constrain risky impacts of product through decreasing or eliminating wastes along supply chain as product design, manufacturing process, warehousing and delivery of final product (Peprah et al., 2016). As noted green supplier is a significant part that affecting the successive stages towards achieving Green Supply Chain, in this study, researchers tried to consider environmental and performance dimensions of the supply chain through extensive literature resources and experts’ inputs, that is classified into six categories as follows:
3.METHODOLOGY
This study proposes to use an integrated ISMMICMAC AHPVikor approach as a method to robust the making decision on green supplier selection. All methods were used in this study are based on fuzzy sets to resolve the obscurity and uncertainty of human desicions. The reasons for combining ISMAHPVikor in this study include (Luthra et al., 2017):

ISM is used to identify the influential role of categories, and their subfactors on green supplier selection problem also analyzes the multiple relationships between categories by dismembering them into different levels.

This integration with multifaceted decision analysis systems can deal with complex decisionmaking processes more smoothly and efficiently.

This integrated approach may provide a sensible, logical, and efficient solution in making decisions situations
The framework of this study is shown in Figure 1 Frist, listing the green supplier selection variable based on the studies carried out and introduced categories in the Table 2, the relationship between these categories are identified by Interpretive Structural Modeling. Next, Fuzzy MICMAC analysis used to evaluate the driving and dependence power of each one. Subfactors of the most effective categories (high driving power) are the input of next step. In the second step, the weight of each factor is identified using Fuzzy AHP method which is used in the computing the ranking of the suppliers through Vikor technique in the end. It is also worth mentioning; all calculations are performed on fuzzy sets. It is possible to use different fuzzy numbers in numerous particular positions. Since the trapezoidal fuzzy number (TFN) compared with triangular ones can deal with more general situations, the TFN is used in this case (Do et al., 2015). The detailed methods are used in the study is given by applying in a case study as follows.
3.1.A Review of ISM and Fuzzy MICMAC Analysis Approach
ISM and fuzzy MICMAC method enable study of the green supplier variables’ interaction and their impacts on the problem. ISM is an interactive process which is structured a set of disparate and related elements into a comprehensive systematic model. ISM has the following steps (Jayant and Azhar, 2014).

Step 1: The most efficient variables in green supplier selection are identified and listed.

Step 2: Establish the contextual relationship between each pair of the identified variables.

Step 3: Formulate a structural selfinteraction matrix (SSIM); the pairwise relationship between variables of the problem is represented by SSIM.

Step 4: Formulate the reachability matrix using SSIM, and checking the transitivity of the matrix. Transitivity is an initial assumption in the ISM technique, which statuses that if a variable ‘A’ is related to ‘B’ and ‘B’ is related to ‘C,’ then ‘A’ is related to ‘C.’ The final reachability matrix M is determined by Equation (1)

Step 5: Partition the final reachability matrix into different levels.

Step 6: Draw a graph based on the final reachability matrix, and the partition levels that is called directed graph.

Step 7: Removing the transitive links and convert the directed graph to interpretive structural model.

Step 8: Checking the conceptual inconsistencies, and making the essential modifications in the developed ISM model. In the following, the introduction of Fuzzy MICMAC is discussed.
Fuzzy MICMAC analysis:
MICMAC was developed by Duperrin and Godet (1973) to analyze the complex issues. The results of ISM are used as an input for the fuzzy MICMAC analysis to identify the driving and dependence power of green supplier selection variables. In fuzzy MICMAC the analysis can be more enhanced since can analyze the possibility of variables interaction by linguistic terms. This method is conducted as per following steps (Bhosale and Kant, 2016).

Step 1: Binary direct relationship matrix
To use fuzzy MICMAC, a supplementary contribution for identifying communication among the variables is required. This supplementary contribution can be defined by linguistic variables as shown in Table 3. The opinions of decision makers are used to obtain the fuzzy direct relationship matrix (FDRM) which then is overlaid on the binary direct relationship matrix of ISM.

Step 2: Fuzzy MICMAC stabilized matrix
After the formation of fuzzy direct relationship, it is required to constant the obtained fuzzy direct relationship matrix by multiplication of boolean algorithm as follows (Bhosale and Kant, 2016):
$\begin{array}{l}\text{C=A,B=maxk[(min(aik,bkj))]}\\ \hspace{1em}\text{whereA=[aik],andB=[bkj]}\end{array}$
after stabilization of matrix, MICMAC analysis diagram can be drawn where the variables are classified into four clusters. The first cluster is called the “autonomous factors” which involves factors with weak driver and dependence power. The second cluster is called the “dependent factors” which involves factors with weak driver power but high dependence. The third cluster includes the “linkage factors” that have high driving and dependence power, and the fourth cluster, which is called the “independent factors” with high driving power but weak dependence (Bhosale and Kant, 2016).
3.1.1.Fuzzy AHP
Since about FAHP method, much research has been done, in this section just mention the FAHP steps (Rauta et al., 2017):Table 4

Step 1: In this step, the decisionmakers make pairwise comparisons between criteria based on trapezoidal fuzzy numbers and their relative importance as follows (Zheng et al., 2012).

Step 2: The pairwise comparison matrix is established according to the previous step (the decisions opinions matrix).

Step 3: Check consistency of matrix, before computing the weights of each criterion, the consistency of the comparison matrix (decision maker’s opinions) is checked by CR (consistency ratio). It was calculated using equation given as CR = CI/RI (Rauta, 2017).

Step 4: Weight of criteria is calculated based on the pairwise comparison matrix.
3.1.2.Fuzzy Vikor
This method determines the closest solution to the ideal by ranking the alternatives, the solution is named optimal compromise (San Cristóbal, 2011). The Fuzzy vikor has the following steps (Alimohammadlo et al., 2013):

Step 1: The linguistic terms (Table 5) used to develop pairwise comparisons among alternatives and each criterion.

Step 2: Developing a decision matrix. The aggregated ratings of the alternatives are derived from experts’ ratings, and following steps form a decision matrix:

Integration: Solving fuzzy eigenvalues according to the following criteria:(2)

Normalization: pairwise comparisons should be normalized since their dimensions are not equal. In this case, an indicator with the highest value will be assumed as benefit (B) and the lowest one as cost (C).(3)
$$\begin{array}{l}{x}_{ij4}^{+}=\underset{i}{\text{max}}\left\{{x}_{ij4}\right\},\hspace{0.17em}\hspace{0.17em}{C}_{j}\in B\\ {x}_{ij4}^{}=\underset{i}{\text{max}}\left\{{x}_{ij1}\right\},\hspace{0.17em}\hspace{0.17em}{C}_{j}\in C\\ {U}_{ij}=\left\{\left(\frac{{x}_{ij1}}{{x}_{ij4}^{+}},\hspace{0.17em}\frac{{x}_{ij2}}{{x}_{ij4}^{+}},\hspace{0.17em}\frac{{x}_{ij3}}{{x}_{ij4}^{+}},\hspace{0.17em}\frac{{x}_{ij4}}{{x}_{ij4}^{+}}\right)\right\},\hspace{0.17em}{C}_{j}\in benefit\\ {U}_{ij}=\left\{\left(\frac{{x}_{ij1}}{{x}_{ij1}^{}},\hspace{0.17em}\frac{{x}_{ij2}}{{x}_{ij1}^{}},\hspace{0.17em}\frac{{x}_{ij3}}{{x}_{ij1}^{}},\hspace{0.17em}\frac{{x}_{ij4}}{{x}_{ij1}^{}}\right)\right\},\hspace{0.17em}{C}_{j}\in cost\end{array}$$(3) 
Defuzzing and utilizing Vikor: The output numbers from previous will be defuzzed and converted to integers and then ranked.(4)
$$\begin{array}{c}\text{Defuzz}\left({x}_{ij}\right)=\frac{{\displaystyle \int \mu \left(x\right)xdx}}{{\displaystyle \int \mu \left(x\right)dx}}\\ \frac{{\displaystyle {\int}_{{x}_{ij1}}^{{x}_{ij2}}\left(\frac{x{x}_{ij1}}{{x}_{ij2}{x}_{ij1}}\right).xdx}+{\displaystyle {\int}_{{x}_{ij2}}^{{x}_{ij3}}xdx}+{\displaystyle {\int}_{{x}_{ij3}}^{{x}_{ij4}}\left(\frac{{x}_{ij4}x}{{x}_{ij4}{x}_{ij3}}\right).xdx}}{{\displaystyle {\int}_{{x}_{ij1}}^{{x}_{ij2}}\left(\frac{x{x}_{ij1}}{{x}_{ij2}{x}_{ij1}}\right).dx}+{\displaystyle {\int}_{{x}_{ij2}}^{{x}_{ij3}}dx}+{\displaystyle {\int}_{{x}_{ij3}}^{{x}_{ij4}}\left(\frac{{x}_{ij4}x}{{x}_{ij4}{x}_{ij3}}\right).dx}}\\ =\frac{{x}_{ij1}{x}_{ij2}+{x}_{ij3}{x}_{ij4}+\frac{1}{3}{\left({x}_{ij4}{x}_{ij3}\right)}^{2}\frac{1}{3}{\left({x}_{ij2}{x}_{ij1}\right)}^{2}}{{x}_{ij1}{x}_{ij2}+{x}_{ij3}+{x}_{ij4}}\end{array}$$(4)


Step 3: The best (${\text{f}}_{\text{i}}{}^{\text{*}}$) and the worst (${\text{f}}_{\text{i}}{}^{\text{}}$) values of all criteria are determined as follows:
$\begin{array}{l}{\text{f}}_{\text{i}}^{\text{*}}=\text{max}\left({\text{x}}_{\text{ij}}\text{,}\hspace{0.17em}\text{j=1,}\hspace{0.17em}\cdots ,\hspace{0.17em}\text{J}\right),\hspace{0.17em}{\text{f}}_{\text{i}}^{\text{}}\text{=min}\left({\text{x}}_{\text{ij}}\text{,}\hspace{0.17em}\text{j}=1,\hspace{0.17em}\cdots ,\hspace{0.17em}\text{j}\right),\\ \text{if}\hspace{0.17em}{\text{C}}_{\text{i}}\hspace{0.17em}\in \hspace{0.17em}\text{benefit}\end{array}$
$\begin{array}{l}{\text{f}}_{\text{i}}^{\text{*}}=\text{min}\left({\text{x}}_{\text{ij}}\text{,}\hspace{0.17em}\text{j=1,}\hspace{0.17em}\cdots ,\hspace{0.17em}\text{J}\right),\hspace{0.17em}{\text{f}}_{\text{i}}^{\text{}}\text{=max}\left({\text{x}}_{\text{ij}}\text{,}\hspace{0.17em}\text{j}=1,\hspace{0.17em}\cdots ,\hspace{0.17em}\text{j}\right),\\ \text{if}\hspace{0.17em}{\text{C}}_{\text{i}}\hspace{0.17em}\in \hspace{0.17em}\text{cost}\end{array}$

Step 4: Determine the values of S_{j}, R_{j}, and Q_{j} by following Equations:(5)(6)
$${S}_{j}={\displaystyle \sum _{j=1}^{n}\frac{{w}_{j}\left({f}_{i}^{*}{f}_{ij}\right)}{\left({f}_{i}^{*}{f}_{i}^{}\right)}},\hspace{0.17em}{R}_{j}=ma{x}_{i}\left(\frac{{w}_{j}\left({f}_{i}^{*}{f}_{ij}\right)}{\left({f}_{i}^{*}{f}_{i}^{}\right)}\right)$$(5)$${Q}_{j}=\left(\frac{v\left({S}_{i}{S}^{*}\right)}{\left({S}^{}{S}^{*}\right)}\right)+\left(\frac{\left(1v\right)\left({R}_{i}{R}^{*}\right)}{\left({R}^{}{R}^{*}\right)}\right)$$(6)which ${S}^{*}=\text{min}\left({S}_{j},\hspace{0.17em}j=1,\hspace{0.17em}\cdots ,\hspace{0.17em}J\right)$, ${S}^{}=\text{max}\left({S}_{j},\hspace{0.17em}j=1,\hspace{0.17em}\cdots ,\hspace{0.17em}J\right)$, ${R}^{*}=\text{min}\left({R}_{j},\hspace{0.17em}j=1,\hspace{0.17em}\cdots ,\hspace{0.17em}J\right)$, ${R}^{}=\text{max}\left({R}_{j},\hspace{0.17em}j=1,\hspace{0.17em}\cdots ,\hspace{0.17em}J\right)$; and v is defined as a weight for the strategy of maximum group utility that is assumed “v = 0.5” in this study (Shemshadi et al., 2011).

Step 5: The alternatives are ranked by sorting in the minimum values of S, R and Q.

Step 6: If the following two conditions are satisfied concomitantly, then the alternative with a minimum value of Q in ranking is considered as the optimal compromise solution (Rostamzadeh et al., 2015):

C1: The alternative Q(A^{(1)}) has an acceptable advantage if Q(A^{(2)})Q(A^{(1)}) ≥ 1/(n1), where A(2) is the alternative with the second position in the ranking list and n is the number of alternatives.

C2: The alternative Q(A^{(1)}) is stable in the decisionmaking process if it is also best ranked in Si and R_{i}.

3.2.Application of Integrated Method in a Case
Here to demonstrate the application of the proposed framework a case study is discussed, which is trying to select the best green supplier among existed alternatives. Jahan Tormoz Kashan industrial manufacturing company is a brake manufacturer in Iran. This company was established in 1999 and at 2011 JTK decided to develop its production in manufacturing brake pads, brake shoes, brake linings. Asbestos was a common component for brakes pads since of its heat resistance and strength. However, it has potential environmental and occupational health hazards too. These issues lead to regulatory statutory and legislative institutions in Iran is forbidden the use of asbestos in brake pads since 2012. Despite these problems and prevention, the company purchases this part from suppliers. The production of this part is needed to comply with environmental requirements so their suppliers must have green attitudes. The company managers have problem in selecting suppliers. It needs to identify a comprehensive list of criteria and variables are included in the green supplier selection problem which will be helpful in implementing the selection process. Thus, the first step is classified of the study criteria which is discussed in the literature review.Figure 2
In this step, a decision group consists of experts was formed to confirm and classified the problem criteria. As mentioned in the literature review, comprehensive evaluation criteria through existed studies were identified and then by experts opinions is classified into six categories as shown in the Table 2.Figure 3
In this step, decision group used ISM method to find interaction among the categories; then Fuzzy MICMAC analysis is applied to find the driving and dependence power of each subfactor and finalize the study criteria. Due to the limitations of the paper pages in this section and only the results of each method is shown. After the contextual relationship between each pair of the categories is established and reachability matrix is formulated, researchers distinguish the categories level, and partitions that lead to specifying different levels of the interpretive structural modeling which is obtained in following:Table 6
It has been observed from Figure 2, the Company resources and administrative capacity is at the first level of ISM model. This category has the highest driving power so that it can effecting on the other criteria categories of green supplier selection. In the second level, warehousing and performance of supplier exist, but the performance and technology ability category have higher driving power since besides its influence on the upper levels, effects on the financial quality of suppliers. The rest categories, respectively are affected by these. According to the categories influence leverage, it is clear that subfactors of lower categories in the green supplier selection are more important. To finalize the problem criteria, Fuzzy MICMAC is used.
The purpose of MACMAC analysis is to evaluate the driving and dependence of subfactors. In this step decision makers used the pairwise matrix of the subfactors and then by changing linguistic matrix to the fuzzy numerical values and MICMAC steps, driving and dependence power diagram are obtained which is shown as follows:
MICMAC analysis diagram shows, most subfactors of the company resources and performance categories have the highest driving and dependence power in the green supplier selection problem which the most important of them are environmental cost, green design, and green manufacturing, whereas subfactors of social interest categories have placed in the forth cluster. This issue also applies to subfactors of knowledge sharing category. Warehousing and delivery activities and financial quality subfactors are divided into two groups, those with the high driving and dependence power and those with lower driving power. In this study, those subfactors that place in the third cluster are considered as main criteria by decision group, since this cluster has the strongest influences on the problem.
Next step is to evaluate the five alternatives based on the main criteria. The following data is gathered using two steps, firstly, a questionnaire was designed and submitted to suppliers, then, the supplier’s sites were surveyed with second party auditor from the company.
The decision group assigned the pairwise comparisons for criteria. Due to the limitations of the paper pages in this section, only the output is displayed. Consistency ratio is calculated CI = 0.05, CR = 0.096 that is shown the consistency of pairwise matrix. Priority weights of criteria to select green supplier have been summarized in Table 7.
The most effective supplier is selected using vikor analysis and their deviation from the total vikor which is discussed in the following. Regarding the vikor steps at first, the pairwise comparisons among alternatives is developed. Then by changing the linguistic variables into the TFN and following the fuzzy algorithms, a decision matrix is obtained that is shown in the Table 8.
Next, the values of S_{i}, R_{i} and Q_{i} for all suppliers are calculated using Eqs (5~6), the weight of maximum group utility is considered to be v = 0.5. The results are given in the following (Table 9):
Finally, the alternatives are raked based on S, R and Q values in descending order wich are shown in the Table 10. According to the crisp Q index values and the ranking of the suppliers in descending order, the best green supplier founded to be C. also both vikor conditions are satisfied, with means 0.253> = 1/4 and similarly C is the best ranked by R and S.
4.RESULTS
As mentioned earlier, this study has been attempted to reflect supplier selection method based on two dimensions, called environmental and performance. In this line, to track a model more accurately, each dimension has been investigated separately. This allows obtaining more accurate and precise behavior of suppliers for each dimension. In another word, despite the supplier C is selected as best options, but we can not guarantee that it maintains appropriate behavior for each dimension separately. This helps auditor to select a supplier based on its defined specific policy efficiently.
The aggregated results for Vikor Q of suppliers based on each dimension is given in the Table 11, respectively.
Additionally, in the Table 12, we calculate the en  vironmental and performance deviation, respectively and is shown in Figure 4.
More precisely, we arrive simply the deviation value by subtracting the value of Q arisen from dimensional and performance to Q_{t}. From what we have obtained so far it is clear that the supplier C has more important among all respect to performance criteria since it has made zero deviation to Q_{t}. Unsurprisingly, this supplier can not reflect relevance to environmental aspect. As a result, it is ranked as second just after supplier A.
5.CONCLUSION
Due to an increased today’s worries of environmental challenges, having green suppliers has become an important consideration for organizations about their supply chains. These considerations can help them to achieve their environmental goals and a competitive position in the industry. Thus green supplier can play an essential role in organization supply chain. The main objective of this study was to propose an integrated approach in green supplier selection problem using an integrated vikor approach based on fuzzy sets and deviations analysis. To illustrate the proposed framework, a case example of brake pad factory was selected. The ISM method has been utilized to determine the interaction between the categories that was obtained from the classification of influenced factors on green supplier selection then MICMAC analysis was used to finalize the study criteria. AHP method was conducted to compute the weights of criteria, and finally, vikor was applied to selecting the best suppliers. Since, in the green supplier selection problem besides the environmental dimensions, the buyer should note the performance dimensions of alternatives, to analyze more precisely the dimension deviations of vikor value for each supplier was computed. The result was indicated that although supplier “C” was the best ones based on overall dimensions, regard to the dimension deviations Figure 4, this supplier pays more attention to the performance measures than the environmental dimension. It indicates that in applying multicriteria decision making further analysis is needed to achieve desirable supplier. This study also has some limitations such as in definition the criteria, the social dimensions for suppliers are not considered as effective factors. Also, the relationship model among the identified factors has not been statistically checked and validated. Structural equation modeling (SEM), has this ability to check the validity of such models with interactions between variables. Thus, this method can be used in the future study to test the validity of this model.