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Pythagorean Fuzzy Muirhead Mean Operators and Their Application in Multiple-Criteria Group Decision-Making

1,* and 1,2
School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756, China
National Laboratory of Railway Transportation, Southwest Jiaotong University, Chengdu 611756, China
Author to whom correspondence should be addressed.
Information 2018, 9(6), 142;
Received: 25 May 2018 / Revised: 5 June 2018 / Accepted: 7 June 2018 / Published: 11 June 2018
PDF [1063 KB, uploaded 11 June 2018]


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. View Full-Text
Keywords: Pythagorean fuzzy set; Muirhead mean; multiple criteria group decision-making Pythagorean fuzzy set; Muirhead mean; multiple criteria group decision-making

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Zhu, J.; Li, Y. Pythagorean Fuzzy Muirhead Mean Operators and Their Application in Multiple-Criteria Group Decision-Making. Information 2018, 9, 142.

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