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Abstract
In this paper we introduce and study the notion of d-continuity continuity on mixed fuzzy topological spaces. We have investigated this notion in the light of the notion of q-neighbourhoods, q-coincidence, fuzzy d-closure, fuzzy d-interior. In this paper we have established the relationship between fuzzy continuity and fuzzy d-continuity in mixed fuzzy topological spaces.
Highlights
The notion of mixed topology has been investigated by Alexiewicz and Semadeni [1]
In this paper we introduce the concepts of δ-continuity in mixed fuzzy topological spaces
An ordinary subset A of X can be regarded as a fuzzy set in X if its membership function is taken as usual characteristic function of A that is μA(x) = 1 for all x ∈ X and μA(x) = 0 for all x ∈ X − A
Summary
The notion of mixed topology has been investigated by Alexiewicz and Semadeni [1]. They have introduced this notion via two normed spaces. A fuzzy set A in a fuzzy topological space (X, τ ) is called a neighborhood of a point x ∈ X if and only if there exists B ∈ τ such that B ⊆ A and A(x) = B(x) > 0. A fuzzy point xλ is called a δ-cluster point of a fuzzy set S in a fuzzy topological spaces (X, τ ) if and only if every regular open Q-neighborhood of xλ is quasi-coincident with S.
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