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

we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

Small sets. We are going to present some results of the following type: under a suitable assumption on a normed space X, each continuous convex function, defined on an open convex set A ⊂ X, is (Gâteaux or Fréchet) differentiable outside a set which is in some sense small. It is natural to ask that a nonempty family S ⊂ 2X whose elements are considered “small sets” satisfy the following conditi...

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy ...