Some Results for Pythagorean Fuzzy Sets

Abstract

Pythagorean fuzzy sets (PFSs), originally proposed by Yager (Yager, Abbasov. Int J Intell Syst 2013;28:436-452), are a new tool to deal with vagueness considering the membership grades are pairs (μ, ν) satisfying the condition μ 2 + ν 2 ≤ 1. As a generalized set, PFSs have close relationship with intuitionistic fuzzy sets (IFSs). PFSs can be reduced to IFSs satisfying the condition μ + ν ≤ 1. However, the related operations of PFSs do not take different conditions into consideration. To better understand PFSs, we propose two operations: division and subtraction, and discuss their properties in detail. Then, based on Pythagorean fuzzy aggregation operators, their properties such as boundedness, idempotency, and monotonicity are investigated. Later, we develop a Pythagorean fuzzy superiority and inferiority ranking method to solve uncertainty multiple attribute group decision making problem. Finally, an illustrative example for evaluating the Internet stocks performance is given to verify the developed approach and to demonstrate its practicality and effectiveness. C 2015 Wiley Periodicals, Inc.

A Novel Approach to Decision-Making with Pythagorean Fuzzy Information

“…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.…”

Energy of Pythagorean Fuzzy Graphs with Applications

“…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].…”

New Operations for Interval-valued Pythagorean Fuzzy Set

“…The PFS has been investigated from different perspectives, including decision making technologies [5][6][7][8][9][10][11][12][13], aggregation operators [14][15][16][17][18][19][20][21][22], information measures [23][24][25] , the extensions of PFS [26][27][28][29][30][31], fundamental properties [32][33][34]. In particular, an extension of PFS named interval-valued Pythagorean fuzzy set (IVPFS) [10,21] is a hot topic at present [35].…”