Some Results for Pythagorean Fuzzy Sets

• Published in: International journal of intelligent systems Vol. 30; no. 11; pp. 1133 - 1160
• Main Authors: Peng, Xindong, Yang, Yong
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01-11-2015; Hindawi Limited
• Subjects: Agglomeration; Division; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Intelligent systems; Internet; Operators; Raw materials
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.21738

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 μ2+ν2≤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.