Pythagorean fuzzy Muirhead mean operators and their application in multiple-criteria group decision-making

Abstract

As a generalization of the intuitionistic fuzzy set (IFS), a Pythagorean fuzzy set has more flexibility than IFS in expressing uncertainty and fuzziness in the process of multiple criteria group decision-making (MCGDM). Meanwhile, the prominent advantage of the Muirhead mean (MM) operator is that it can reflect the relationships among the various input arguments through changing a parameter vector. Motivated by these primary characters, in this study, we introduced the MM operator into the Pythagorean fuzzy context to expand its applied fields. To do so, we presented the Pythagorean fuzzy MM (PFMM) operators and Pythagorean fuzzy dual MM (PFDMM) operator to fuse the Pythagorean fuzzy information. Then, we investigated their some properties and gave some special cases related to the parameter vector. In addition, based on the developed operators, two MCGDM methods under the Pythagorean fuzzy environment are proposed. An example is given to verify the validity and feasibility of our proposed methods, and a comparative analysis is provided to show their advantages.