On some weaker hesitant fuzzy open sets

Abstract

The purpose of this paper is to define and study some new types of hesitant fuzzy open sets namely, hesitant fuzzy αα-open, hesitant fuzzy preopen, hesitant fuzzy semiopen, hesitant fuzzy b-open and hesitant fuzzy ββ-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.