Abstract
A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets ( SFS ) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries.
Highlights
The membership function is used to define the fuzzy set (F S)
Yager [20,21] defines the Pythagorean fuzzy sets P yF S, which is the successful extension of intuitionistic fuzzy sets, by putting a new condition on positive membership ξ and negative membership functions ν, i.e., 0 ≤ ξ 2 + ν2 ≤ 1
Ashraf [26,27,28] defines the spherical fuzzy sets SF S s, which is the successful extension of picture fuzzy sets and P yF S, by putting a new condition on positive membership ξ, neutral membership η and negative membership functions ν, i.e., 0 ≤ ξ 2 + η 2 + ν2 ≤ 1
Summary
The membership function is used to define the fuzzy set (F S). The uncertainty model effectively by the fuzzy set theory define by Zadeh [1]. Khan et al [12] define the generalized picture fuzzy soft set and applied them to decision-making problems. Yager [20,21] defines the Pythagorean fuzzy sets P yF S , which is the successful extension of intuitionistic fuzzy sets, by putting a new condition on positive membership ξ and negative membership functions ν, i.e., 0 ≤ ξ 2 + ν2 ≤ 1. Ashraf [26,27,28] defines the spherical fuzzy sets SF S s, which is the successful extension of picture fuzzy sets and P yF S , by putting a new condition on positive membership ξ, neutral membership η and negative membership functions ν, i.e., 0 ≤ ξ 2 + η 2 + ν2 ≤ 1.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call