Some Results for Pythagorean Fuzzy Sets

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 (mu, nu) satisfying the condition mu(2) + nu(2) <= 1. As a generalized set, PFSs have close relationship with intuitionistic fuzzy sets (IFSs). PFSs can be reduced to IFSs satisfying the condition mu + nu <= 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.