Premium
Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making
Author(s) -
Zeng Wenyi,
Li Deqing,
Yin Qian
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22027
Subject(s) - pythagorean theorem , ranking (information retrieval) , mathematics , degree (music) , similarity (geometry) , fuzzy logic , point (geometry) , pythagorean triple , group decision making , fuzzy set , artificial intelligence , group (periodic table) , data mining , computer science , chemistry , geometry , organic chemistry , image (mathematics) , physics , acoustics , political science , law
The main feature of Pythagorean fuzzy sets is that it is characterized by five parameters, namely membership degree, nonmembership degree, hesitancy degree, strength of commitment about membership, and direction of commitment. In this paper, we first investigate four existing comparison methods for ranking Pythagorean fuzzy sets and point out by examples that the method proposed by Yager, which considers the influence fully of the five parameters, is more efficient than the other ones. Later, we propose a variety of distance measures for Pythagorean fuzzy sets and Pythagorean fuzzy numbers, which take into account the five parameters of Pythagorean fuzzy sets. Based on the proposed distance measures, we present some similarity measures of Pythagorean fuzzy sets. Furthermore, a multiple criteria Pythagorean fuzzy group decision‐making approach is proposed. Finally, a numerical example is provided to illustrate the validity and applicability of the presented group decision‐making method.