Abstract
The concept of a fuzzy topology on a fuzzy set has been introduced in [1]. The aim of this work is to introduce fuzzy δ*-continuity and fuzzy δ**-continuity in this in new situation and to show the relationships between fuzzy continuous functions where we confine our study to some of their types such as, fuzzy δ-continuity, fuzzy continuity, after presenting the definition of a fuzzy topology on a fuzzy set and giving some properties related to it.
Highlights
The concept of a fuzzy topology on a fuzzy set has been introduced by Chakrabarty and Ahsanullah [1]
We introduce the concepts of a fuzzy δ*-continuity, fuzzy δ**continuity and to show the relationships between types of fuzzy continuous functions in this situation and we examine the validity of the standard results
The main purpose of this paper introduces a new concept in fuzzy set theory, namely that of a fuzzy δ*-continuity and fuzzy δ**-continuity
Summary
The concept of a fuzzy topology on a fuzzy set has been introduced by Chakrabarty and Ahsanullah [1]. The concepts of fuzzy δ-closed sets, fuzzy δ-open sets fuzzy regular open, fuzzy regular closed, fuzzy δcontinuity and the relation between fuzzy continuity and fuzzy δ-continuity in this new situation was introduced by Zahran [3]. These functions have been characterized and investigated mainly in light of the notions of quasineighborhood, quasi-coincidence. We introduce the concepts of a fuzzy δ*-continuity, fuzzy δ**continuity and to show the relationships between types of fuzzy continuous functions in this situation and we examine the validity of the standard results
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