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
Summary
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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