Fermatean Fuzzy Schweizer–Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

Dongmei Wei · Yuan Rong · Yi Liu · Harish Garg · Dragan Stevan Pamucar

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Multi-Criteria Decision Making Optimization and Mathematical Programming Fuzzy and Soft Set Theory

Abstract

The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer-Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches.

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References

1965Fuzzy sets 1986Intuitionistic fuzzy sets 2013Pythagorean Membership Grades in Multicriteria Decision Making 2015Best-worst multi-criteria decision-making method: Some properties and a linear model 2013Pythagorean Membership Grades, Complex Numbers, and Decision Making 2018A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems 2019Fermatean fuzzy sets 2016Green supplier selection using fuzzy group decision making methods: A case study from the agri-food industry

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