Evidential Fermatean fuzzy multicriteria decision‐making based on Fermatean fuzzy entropy

Abstract

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.