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Evidential Fermatean fuzzy multicriteria decision‐making based on Fermatean fuzzy entropy
Author(s) -
Deng Zhan,
Wang Jianyu
Publication year - 2021
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22534
Subject(s) - entropy (arrow of time) , fuzzy logic , mathematics , fuzzy number , data mining , fuzzy set , fuzzy classification , artificial intelligence , fuzzy set operations , defuzzification , fuzzy measure theory , computer science , mathematical optimization , machine learning , physics , quantum mechanics
Fermatean fuzzy set (FFS) is an effective tool to depict expert reasoning information in the decision‐making process. In this study, we first propose a novel Fermatean fuzzy entropy measure to describe the fuzziness degree of FFSs. The new Fermatean fuzzy entropy takes into account the uncertainty information and the indeterminacy degree of FFSs. Subsequently, we prove that Fermatean fuzzy entropy satisfies the axiom requirement of fuzzy entropy measure. Thereafter, a novel Fermatean fuzzy multicriteria decision‐making approach is developed based on Dempster–Shafer theory with the help of the Fermatean fuzzy entropy. The proposed method modeled each Fermatean fuzzy number as a piece of evidence, and the weights of criteria are determined by the entropy measure of FFSs. Then, the weighted average evidence for the alternatives under all criteria is computed from the weights of criteria. Later, Dempster's combination rule is leveraged to combine the weighted average evidence of the alternatives to obtain the final evaluation information about each alternative. The proposed approach can effectively deal with the uncertain information in decision‐making problems and help reduce the information loss in the decision‐making process. Ultimately, the feasibility and validity of the proposed approach are demonstrated through two practical instances.