Some Results for Pythagorean Fuzzy Sets

By Xindong Peng, Yong Yang. International Journal of Intelligent Systems, 2015

840 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Management, Monitoring, Policy and Law, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/18457bbebc5d94d7a74a3f888ce2dbb1c0ca9963

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In Control and Systems Engineering

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Citations in the corpus

A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making (2016, background): “Recently, Peng and Yand 16 deﬁned the new operations such as division, subtraction, and their corresponding properties.”
Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators (2016, background): “Peng and Yang 21 discussed their relationship and proposed a superiority and inferiority ranking multiple attribute group decision-making (MAGDM) method.”
Pythagorean Fuzzy Information Measures and Their Applications (2017, methodology): “Peng and Yang 16 discussed their relationship and proposed a superiority and inferiority ranking multiple attribute group decision making (MAGDM) method.”
A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem (2016, neutral): “Peng and Yang [19] deﬁned the new operations such as division; subtraction and their corresponding properties on PFNs. Recently, Garg [14] proposed a new generalized Pythagorean fuzzy information aggregation operators using Einstein operations.”
Pythagorean fuzzy set: state of the art and future directions (2017, background): “Theorem 2.10 (Peng and Yang 2015) Let p1 = (μP1 , νP1), p2 = (μP2 , νP2) be two PFNs, then (1) pc1 ∪ pc2 = (p1 ∩ p2)c; (2) pc1 ∩ pc2 = (p1 ∪ p2)c; (3) pc1 ⊕ pc2 = (p1 ⊗ p2)c; (4) pc1 ⊗ pc2 = (p1 ⊕ p2)c; (5) pc1 pc2 = (p1 p2)c, if νP1 ≥ νP2 , μP1 ≤ min { μP2 , μP2πP1 πP2 } ; (6) pc1 pc2 = (p1 p2)c,…”
An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets (2019, neutral): “2-dimensional, while here we have 3-dimensional space due to the number of components in SFS [29].”
Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems (2019, neutral): “Many researchers have studied fuzzy set theory, soft set theory, m-polar fuzzy set theory, Pythagorean fuzzy set theory and their applications in real life problems (see [52–62]).”
Multiple-Attribute Decision-Making Based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers (2019, methodology): “[30] X. Peng and Y. Yang, “Some results for Pythagorean fuzzy sets,” Int.”