Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

Abstract

Recently, a new model based on Pythagorean fuzzy set (PFS) has been presented to manage the uncertainty in real‐world decision‐making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision‐making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.

A Novel Approach to Decision-Making with Pythagorean Fuzzy Information

“…To capture more useful information under imprecise and uncertain circumstances, Yager [4][5][6] recently proposed the concept of Pythagorean fuzzy set (PFS) as a new evaluation format, which is characterized by the membership and the non-membership degree satisfying the condition that their square sum is not greater than 1. Zhang and Xu [7] provided the detailed mathematical expression for PFS and put forward the concept of Pythagorean fuzzy number (PFN). The PFS is more general than the IFS because the space of PFS's membership degree is greater than the space of IFS's membership degree.…”

“…For this case, the PFS shows its wider applicability than the IFS. PFSs as a novel evaluation have been prosperously applied in various fields, such as the internet stocks investment [8], the service quality of domestic airline [7] and the governor selection of the Asian Infrastructure Investment Bank [9]. A graph is a convenient way of interpreting information involving the relationship between objects.…”

MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making

“…On the other hand, the Pythagorean fuzzy set (PFS) [29][30][31][32] has arisen as an operational instrument for handling the vagueness of MCDM problems. The PFS is categorized by means of the affiliation degree and the nonaffiliation degree, whose sum of squares is less than or equal to 1.…”

Energy of Pythagorean Fuzzy Graphs with Applications

“…The prominent characteristic of the Pythagorean fuzzy model is to relax the condition that the sum of its membership degree and non-membership degree is no greater than one with the square sum of its membership degree and non-membership degree no greater than one. After the inception of PFS by Yager [2], Zhang and Xu [4] presented the mathematical form of the PFS and introduced the concept of the Pythagorean fuzzy number (PFN). Meanwhile, they presented a series of basic operational laws of PFNs and proposed the Pythagorean fuzzy aggregation operators.…”

“…Meanwhile, they presented a series of basic operational laws of PFNs and proposed the Pythagorean fuzzy aggregation operators. PFS, a novel class of the non-standard fuzzy set, has a wide range of applications in different fields, such as medical diagnosis [5], Internet stock investment [6], the service quality of domestic airlines [4] and the governor selection of the Asian Infrastructure Investment Bank [7].…”