Abstract

The purpose of this paper is to define and study some new types of hesitant fuzzy open sets namely, hesitant fuzzy α α -open, hesitant fuzzy preopen, hesitant fuzzy semiopen, hesitant fuzzy b-open and hesitant fuzzy β β -open in hesitant fuzzy topological space. Some properties and the relationships between these hesitant fuzzy sets are investigated. Furthermore, some relationships between them in hesitant fuzzy subspace are introduced.

Highlights

  • Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set

  • In 2010, Torra [14] introduced the notion of a hesitant fuzzy set as an extension of a fuzzy set

  • Divakaran and John [4] introduced a basic version of hesitant fuzzy rough sets through hesitant fuzzy relations

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Summary

Introduction

Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set. (7) the union of {hi}i∈N, denoted by defined as follows: for each x ∈ X, i∈Nhi, is a hesitant fuzzy set in X (4) Every hesitant fuzzy preopen set is hesitant fuzzy b-open.

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