Fuzzy weakly preclosed functions between fuzzy topological spaces

Abstract EN

Many researchers introduced and characterize fuzzy sets, Prof.

Zadeh (1965) introduced the concept of fuzzy sets, much attention has been paid in order to generalize the basic concept of classical topology in fuzzy setting and thus a modern theory of fuzzy topology is developed .In (1985) D.

A.

Rose defined weakly open functions in topological spaces, J.

H.

Park, Y.

B.

Park and J.

S.

Park (1997) introduced the notion of weakly open functions in between fuzzy topological spaces.

In this paper we discuss the concept of fuzzy weakly preclosed functions.

By (X, τ) we mean a fuzzy topological space (fts) due to Chang.

A fuzzy point χ ∈ X with p (0 < p ≤ 1) is denoted by χp.

Two fuzzy sets λ and β are called quasi-coincident denoted by λ q β if ∃ χ ∈ X ∋ λ (χ) + β (χ) > 1 and if it is not quasicoincident it denoted by q.

λ ≤ β iff λ q (1-β).

A fuzzy set λ is said to q-neighborhood (q-nbd) of xp if there is a fuzzy open set µ such that χ p q µ.[8] If λ be a fuzzy set ∈ X, then pCl (λ) = ∩ {β : β ≥λ, β is a fuzzy preclosed} pInt (λ) = ∪ {β : λ ≥ β, β is a fuzzy preopen} is called a fuzzy preclosure of λ.

Let ƒ : (X, τ1) → (Y, τ2) be a function from a fts (X, τ1) into (Y, τ2), the function ƒ is called fuzzy preclosed if ƒ (λ) is a fuzzy preclosed of Y for each fuzzy closed set λ in X.

A function ƒ : (X, τ1) → (Y, τ2) is said to be fuzzy weakly preclosed if pCl(ƒ (Int (β))) ≤ ƒ (β) for each fuzzy closed subset β of X.

A function ƒ : (X, τ1) → (Y, τ2) is called fuzzy contra-closed if ƒ (λ) is a fuzzy open set in Y for each fuzzy closed set λ in X .

In this paper some modification on the fuzzy preclosed functions between topologies is presented and the conclusions are listed at the end.