Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making. Issue 11 (27th July 2018)

• Record Type: Journal Article
• Authors: Zeng, Wenyi; Li, Deqing; Yin, Qian
• Is Part Of: International journal of intelligent systems. Volume 33:Issue 11(2018)
• Page Start: 2236
• Page End: 2254
• Publication Date: 2018-07-27
• Subjects: distance measure -- group decision making -- intuitionistic fuzzy sets -- Pythagorean fuzzy sets -- similarity measure; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; 006.3
• DOI: 10.1002/int.22027
• Languages: English
• ISSNs: 0884-8173

Abstract

Abstract: 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.