Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making

Abstract

The main feature of Pythagorean fuzzy sets is that it is characterized by five parameters, namely membership degree, nonmembership degree, hesitancy degree, strength of commitment about membership, and direction of commitment. In this paper, we first investigate four existing comparison methods for ranking Pythagorean fuzzy sets and point out by examples that the method proposed by Yager, which considers the influence fully of the five parameters, is more efficient than the other ones. Later, we propose a variety of distance measures for Pythagorean fuzzy sets and Pythagorean fuzzy numbers, which take into account the five parameters of Pythagorean fuzzy sets. Based on the proposed distance measures, we present some similarity measures of Pythagorean fuzzy sets. Furthermore, a multiple criteria Pythagorean fuzzy group decision‐making approach is proposed. Finally, a numerical example is provided to illustrate the validity and applicability of the presented group decision‐making method.

Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision‐making

“…Basic concepts of PFSs are briefly reviewed in this section. [53][54][55][56][57][58][59][60][61] Definition 2.1. A PFSh over the universe of discourse X interpreted as…”

On some correlation coefficients in Pythagorean fuzzy environment with applications

“…A new measure of distance for PFSs was developed by Peng and Dai . By considering five parameters, namely degree of membership, degree of nonmembership, degree of hesitation, commitment strength about membership, and direction of commitment, Zeng et al developed a variety of measures of distance for PFNs. By combining the FS‐theory with linguistic term sets (LTSs), Garg introduced the concept of the linguistic Pythagorean fuzzy set (LPFS).…”

Some q ‐rung orthopair fuzzy Hamy mean operators in multiple attribute decision‐making and their application to enterprise resource planning systems selection

“…More recently, Pythagorean fuzzy set (PFS) has appeared as an effective and useful tool for depicting uncertainty of the multiple attribute decision‐making (MADM) problems . The PFS is also characterized by the membership degree and the nonmembership degree, whose sum of squares is less than or equal to 1, and the PFS is more general than intuitionistic fuzzy set (IFS) .…”

“…Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.K E Y W O R D S enterprise resource planning system, multiple attribute decisionmaking, Pythagorean fuzzy set, q-rung orthopair fuzzy sets, q-rung orthopair fuzzy weighted dual Hamy mean operator, q-rung orthopair fuzzy weighted Hamy mean operator 1 | INTRODUCTION More recently, Pythagorean fuzzy set (PFS) 1 has appeared as an effective and useful tool for depicting uncertainty of the multiple attribute decision-making (MADM) problems. [2][3][4][5][6][7][8] The PFS is also characterized by the membership degree and the nonmembership degree, whose sum of squares is less than or equal to 1, and the PFS is more general than intuitionistic fuzzy set (IFS). [9][10][11][12][13][14][15][16][17] In some cases, the PFS can solve some problems that the IFS cannot, for example, if a DM gives the membership degree and the nonmembership degree as 0.8 and 0.6, respectively; then it is only valid for the PFS.…”