Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean

Wuhuan Xu,Xiaopu Shang,Jun Wang

doi:10.1007/s40747-020-00255-z

Abstract

The linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.

Highlights

In modern economic and social management activities, we have to face quite a few multi-attribute group decisionmaking (MAGDM) problems
It is noted that the cubic linguistic Pythagorean fuzzy power average (CLPFPA) and cubic linguistic Pythagorean fuzzy power weighted average (CLPFPWA) operators have the ability of reducing the negative influence of unreasonable cubic linguistic Pythagorean fuzzy value (CLPFV) on the final results
Our proposed method is based on the CLPFPWA and CLPFPWHM, which implies that our multiple attribute group decision-making (MAGDM) method can effectively deal with decision makers (DMs)’ unreasonable or irrational bias, making the final decisions more reasonable

Summary

Introduction

In modern economic and social management activities, we have to face quite a few multi-attribute group decisionmaking (MAGDM) problems. For the usage of CLPFSs in practical MAGDM problems, we further give basic operational rules of CLPFSs and based on which, a series of cubic linguistic Pythagorean fuzzy AOs are proposed. (4) ak 1⁄4 stðh=tÞk ; stðs=tÞk ; stpffi1ffiÀffiffiffiðffi1ffiffiÀffiffirffiffi2ffiffi=ffitffi2ffiffiÞffikffi; stpffi1ffiÀffiffiffiðffi1ffiffiÀffiffieffiffi2ffi=ffiffitffi2ffiÞffiffik ; k [ 0: We provide the following comparison method to rank any two ULPFVs. Definition 4 Let a 1⁄4 ð1⁄2sh; ss; 1⁄2sr; seÞ be an ULPFV dSee1⁄4finÈedsbs0 on sb the Élinguistic term set st; b 2 1⁄20; t , the score function of a is defined as. Example 3 Let g1 1⁄4 hð1⁄2s4; s5; 1⁄2s1; s2Þ; ðs; s5Þi and g2 1⁄4 hð1⁄2s1; s3; 1⁄2s4; s5Þ; ðs; s4Þi be two CLPFVs defined on the s6; b 2 1⁄20; 6 , we can calculate the distance between g1 and g2, PHMðkÞða; a2; :::; anÞ 1X

42 À 12 þ 52 À 32 þ 12 À 42 þ 22 À 52 þ 32 À 32 þ 52 À 42

Methods

Conclusions

Findings

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