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Linguistic terms and their corresponding interval type-2 fuzzy sets. Table 1

Table 1 Linguistic terms and their corresponding interval type-2 fuzzy sets. Table 1

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Fig. 2. The framework for using the proposed approach. modification is performed in the WPM process of the proposed approach to avoid calculations with complex numbers. In the proposed approach, we use a procedure for calculation of criteria weights in which the weights expressed by decision-makers are combined with the weights resulted from the entropy method. We can obtain more realistic criteria weights for decision-making process by using this combination. Using IT2FSs gives more de- grees of flexibility to the decision-makers to express their prefer- ences in an uncertain environment. The framework for using the proposed approach is represented in Fig. 2.
Fig. 2. The framework for using the proposed approach. modification is performed in the WPM process of the proposed approach to avoid calculations with complex numbers. In the proposed approach, we use a procedure for calculation of criteria weights in which the weights expressed by decision-makers are combined with the weights resulted from the entropy method. We can obtain more realistic criteria weights for decision-making process by using this combination. Using IT2FSs gives more de- grees of flexibility to the decision-makers to express their prefer- ences in an uncertain environment. The framework for using the proposed approach is represented in Fig. 2.
The average decision matrix (X).
The average decision matrix (X).
Step 5. The average subjective weight of each criterion is calculated based on Step 4 and Eq. (27). The results are shown in Table 5. Cinwn EC Dacanrl nn Crank 9 Takla GC ana Br (9O@N <axecrawm pou lowlatectha
Step 5. The average subjective weight of each criterion is calculated based on Step 4 and Eq. (27). The results are shown in Table 5. Cinwn EC Dacanrl nn Crank 9 Takla GC ana Br (9O@N <axecrawm pou lowlatectha
The average subjective weights of criteria. Table 5
The average subjective weights of criteria. Table 5
The aggregated weights of criteria. Table 6
The aggregated weights of criteria. Table 6
Table 4 (continued )
Table 4 (continued )
The normalized decision matrix.
The normalized decision matrix.
a The values of WPM measure (Q;_) for each alternative. Table 9
a The values of WPM measure (Q;_) for each alternative. Table 9
Losi sa 7 The values of WSM measure (Q;_) for each alternative. Table 8
Losi sa 7 The values of WSM measure (Q;_) for each alternative. Table 8
Table 7 (continued ) Step 10 and 11. Based on Table 10, Table 11 and Eq. (34), we can calculate the WASPAS measure for each alternative (with A = 0.5). Table 12 shows the values of Q; and the corresponding crisp score values. According to this table, the ranking order of alternatives is A> Ag > A> A> AG > A> A 5 >A 4. Therefore, 7 is the best alternative. aggregated weights of criteria (with 6 = 0.5). Table 6 represents the results of this step.
Table 7 (continued ) Step 10 and 11. Based on Table 10, Table 11 and Eq. (34), we can calculate the WASPAS measure for each alternative (with A = 0.5). Table 12 shows the values of Q; and the corresponding crisp score values. According to this table, the ranking order of alternatives is A> Ag > A> A> AG > A> A 5 >A 4. Therefore, 7 is the best alternative. aggregated weights of criteria (with 6 = 0.5). Table 6 represents the results of this step.
The scaled values of WSM measure (Q; ~) for each alternative. Table 10
The scaled values of WSM measure (Q; ~) for each alternative. Table 10
bone ieee? 2 The scaled values of WPM measure (Q; _) for each alternative.
bone ieee? 2 The scaled values of WPM measure (Q; _) for each alternative.
The calculated WASPAS measure (Q;) and the corresponding crisp score values.
The calculated WASPAS measure (Q;) and the corresponding crisp score values.
Interpretation of the correlation values (r;).
Interpretation of the correlation values (r;).
Ranking of the alternatives with different methods and the corresponding correla- tion (r;). Fig. 3. Seven sets of the criteria weights for sensitivity analysis. Table 14 analysis. We name these methods M-1 to M-6, respectively and the illustrative example is solved using them. To compare the results of the proposed approach with the other methods, we use the Spearman's rank correlation coefficient (rs) (Zavadskas et al., 2014). Table 13 shows the interpretation of different values of r; (Walters, 2009). According to this table, when the values of r; are greater than 6. Discussion
Ranking of the alternatives with different methods and the corresponding correla- tion (r;). Fig. 3. Seven sets of the criteria weights for sensitivity analysis. Table 14 analysis. We name these methods M-1 to M-6, respectively and the illustrative example is solved using them. To compare the results of the proposed approach with the other methods, we use the Spearman's rank correlation coefficient (rs) (Zavadskas et al., 2014). Table 13 shows the interpretation of different values of r; (Walters, 2009). According to this table, when the values of r; are greater than 6. Discussion
Ranking results with different sets of criteria weights and different parameters. Table 15 Multi-criteria decision-making methods have been widely used in the field of green supply chain management (Govindan et al., 2015). This study has considered the process of multi-criteria evaluation of green suppliers within the context of interval type-
Ranking results with different sets of criteria weights and different parameters. Table 15 Multi-criteria decision-making methods have been widely used in the field of green supply chain management (Govindan et al., 2015). This study has considered the process of multi-criteria evaluation of green suppliers within the context of interval type-
Correlation (r;) between ranking results with different sets of criteria weights and different parameters. Table 16
Correlation (r;) between ranking results with different sets of criteria weights and different parameters. Table 16
References using a procedure for obtaining more realistic weights of criteria and increasing the stability of method. However, transforming the non-beneficial criteria to beneficial criteria by normalization is the main disadvantage of the proposed approach. Improving the method with respect to this disadvantage could be performed in the future researches. The proposed approach can be used for any problems that have the common structure of MCDM problems and use interval type-2 fuzzy information. Although this study has focused on problem with subjective criteria, the proposed approach can be used in a general situation. For the future researches, we suggest using some objective criteria and application of the pro- posed approach in other MCDM problems.
References using a procedure for obtaining more realistic weights of criteria and increasing the stability of method. However, transforming the non-beneficial criteria to beneficial criteria by normalization is the main disadvantage of the proposed approach. Improving the method with respect to this disadvantage could be performed in the future researches. The proposed approach can be used for any problems that have the common structure of MCDM problems and use interval type-2 fuzzy information. Although this study has focused on problem with subjective criteria, the proposed approach can be used in a general situation. For the future researches, we suggest using some objective criteria and application of the pro- posed approach in other MCDM problems.
Related topics:
Supply Chain ManagementDecision MakingJudgment and decision makingDecision Making Under UncertaintyMulti Criteria Decision MakingDecision TheorySustainable Supply ChainPurchasing and Supply ManagementSupply Chain Risk ManagementGreen Supply Chain Management
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