(3, 2)-Fuzzy Sets and Their Applications to Topology and Optimal Choices.

Hariwan Z Ibrahim,O G Elbarbary,Tareq M Al-Shami,Ahmed Mostafa Khalil

doi:10.1155/2021/1272266

Hariwan Z Ibrahim, O G Elbarbary + Show 2 more

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https://doi.org/10.1155/2021/1272266

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Abstract

The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

Highlights

E idea of intuitionistic fuzzy sets suggested by Atanassov [5] is one of the extensions of fuzzy sets with better applicability
Olgun et al [14] presented the concept of Pythagorean fuzzy topological spaces and Ibrahim [15] defined the concept of Fermatean fuzzy topological spaces
We prove that τ1 is the coarsest (3, 2)-fuzzy topology over X such that f is (3, 2)-fuzzy continuous

Summary

Introduction

E idea of intuitionistic fuzzy sets suggested by Atanassov [5] is one of the extensions of fuzzy sets with better applicability. 3. Topology with respect to (3, 2)-Fuzzy Sets Let τ be a family of (3, 2)-fuzzy subsets of a non-empty set X. Let (X, τ) be a (3, 2)-fuzzy topological space and D 􏼈〈x, αD(x), βD(x)〉: x ∈ X􏼉 be a (3, 2)-FS in X.

Results

Conclusion