Title: New similarity measures for Pythagorean fuzzy sets with applications

Authors: Paul Augustine Ejegwa

Addresses: Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria

Abstract: The concept of Pythagorean fuzzy sets (PFSs) is pertinent in finding reliable solution to decision-making problems, because of its unique nature of indeterminacy. Pythagorean fuzzy set is characterised by membership degree, non-membership degree, and indeterminate degree in such a way that the sum of the square of each of the parameters is one. The objective of this paper is to present some new similarity measures for PFSs by incorporating the conventional parameters that describe PFSs, with applications to some real-life decision-making problems. Furthermore, an illustrative example is used to establish the applicability and validity of the proposed similarity measures and compare the results with the existing comparable similarity measures to show the effectiveness of the proposed similarity measures. While analysing the reliability of the proposed similarity measures in comparison to analogous similarity measures for PFSs in literature, we discover that the proposed similarity measures, especially, s₄ yields the most reasonable measure. Finally, we apply s₄ to decision-making problems such as career placement, medical diagnosis, and electioneering process. Additional applications of these new similarity measures could be exploited in decision making of real-life problems embedded with uncertainty such as in multi-criteria decision-making (MCDM) and multi-attribute decision-making (MADM), respectively.

Keywords: fuzzy set; intuitionistic fuzzy set; similarity measure; Pythagorean fuzzy set.

DOI: 10.1504/IJFCM.2020.106105

International Journal of Fuzzy Computation and Modelling, 2020 Vol.3 No.1, pp.75 - 94

Received: 06 Feb 2019
Accepted: 08 Aug 2019
Published online: 30 Mar 2020 *