New similarity measure and distance measure for Pythagorean fuzzy set

Xindong Peng

doi:10.1007/s40747-018-0084-x

Abstract

Pythagorean fuzzy set (PFS), disposing the indeterminacy portrayed by membership and non-membership, is a more viable and effective means to seize indeterminacy. Due to the defects of existing Pythagorean fuzzy similarity measures or distance measures (cannot obey third or fourth axiom; have no power to differentiate positive and negative difference; have no power to deal the division by zero problem), the major key of this paper is to explore the novel Pythagorean fuzzy distance measure and similarity measure. Meanwhile, some interesting properties of distance measure and similarity measure are proved. Some counterintuitive examples are presented to state their availability of similarity measure among PFSs.

Highlights

Pythagorean fuzzy sets (PFSs) [2], initiatively introduced by Yager, have regarded as an efficient tool to describe the vagueness of the MADM issues
If a DM or expert presents the degree of nonmembership and membership as 0.5 and 0.7, respectively, it is just efficacious for the PFSs
All the IFSs are a part of the PFSs, which reveals that the PFSs are more forceful for solving the indeterminate issues

Summary

Introduction

Pythagorean fuzzy sets (PFSs) [2], initiatively introduced by Yager, have regarded as an efficient tool to describe the vagueness of the MADM issues. If a DM or expert presents the degree of nonmembership and membership as 0.5 and 0.7, respectively, it is just efficacious for the PFSs. That is to say, all the IFSs are a part of the PFSs, which reveals that the PFSs are more forceful for solving the indeterminate issues. Zhang and Xu [3] presented the particular mathematical language expression for PFSs and defined notion of PFN. They continued to propose a revised Pythagorean fuzzy TOPSIS (PF-TOPSIS) for dealing with the MCDM issue with PFNs. Peng and Yang [4] explored the subtraction and division operations for PFNs and initiated a Pythagorean fuzzy SIR (PF-SIR) algorithm to handle multi-criteria group decision-making (MCGDM) issue. Some extension models [5,6,7,8] of PFSs are

B Xindong Peng

Conclusion

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