Fermatean fuzzy linguistic set and its application in multicriteria decision making

Donghai Liu · Yuanyuan Liu

121 citations0/0 files storedInternational Journal of Intelligent Systems

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

Abstract

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter in the proposed distance measure is also discussed.

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References

1965Fuzzy sets 1986Intuitionistic fuzzy sets 2013Pythagorean Membership Grades in Multicriteria Decision Making 1975The concept of a linguistic variable and its application to approximate reasoning—II 2006Some geometric aggregation operators based on intuitionistic fuzzy sets 2011Multiple Attribute Decision Making 2014Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets 2003A method based on linguistic aggregation operators for group decision making with linguistic preference relations*1

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