Abstract
Due to the increased complexity of real decision-making problems, representing attribute values correctly and appropriately is always a challenge. The recently proposed Pythagorean fuzzy set (PFS) is a powerful and useful tool for handling fuzziness and vagueness. The feature of PFS that the square sum of membership and non-membership degrees should be less than or equal to one provides more freedom for decision makers to express their assessments and further results in less information loss. The aim of this paper is to develop some Pythagorean fuzzy aggregation operators to aggregate Pythagorean fuzzy numbers (PFNs). Additionally, we propose a novel approach to multi-attribute group decision-making (MAGDM) based on the proposed operators. Considering the Muirhead mean (MM) can capture the interrelationship among all arguments, and the interaction operational rules for PFNs can make calculation results more reasonable, to take full advantage of both, we extend MM to PFSs and propose a family of Pythagorean fuzzy interaction Muirhead mean operators. Some desirable properties and special cases of the proposed operators are also investigated. Further, we present a novel approach to MAGDM with Pythagorean fuzzy information. Finally, we provide a numerical instance to illustrate the validity of the proposed model. In addition, we perform a comparative analysis to show the superiorities of the proposed method.
Highlights
As one of the most important branches of modern decision-making theory, multi-attribute group decision-making (MAGDM) has been widely investigated and successfully applied to many fields, owing to its high capacity of modelling the process of real decision-making problems [1,2,3,4,5,6]
We explore some special cases of Pythagorean fuzzy interaction Muirhead mean (PFIMM)
Some operators do not take the correlations among attributes into consideration, which cannot satisfy the needs of real decision-making problems
Summary
As one of the most important branches of modern decision-making theory, multi-attribute group decision-making (MAGDM) has been widely investigated and successfully applied to many fields, owing to its high capacity of modelling the process of real decision-making problems [1,2,3,4,5,6]. Zadeh [7] originally introduced the fuzzy set (FS) theory, which makes it possible to describe vagueness and uncertainty. Atanassov [3] put forward the concept of an intuitionistic fuzzy set (IFS), which can express the complex fuzzy information effectively as it simultaneously has a membership degree and a non-membership degree. Considering its effective vagueness information processing capabilities, IFS has been widely investigated and applied to so many fields since its appearance. Ren and Wang [9] proposed a new similarity measure for interval-valued IFSs, Information 2018, 9, 157; doi:10.3390/info9070157 www.mdpi.com/journal/information
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