Abstract
In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like 𝑅𝜏𝑟-closure, 𝑅𝜏𝑟-interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, 𝑞𝛼𝑟-pre-neighborhood, 𝑞𝛼𝑟-pre-clo-sure and 𝑞𝛼𝑟- pre-continuous function in smooth fuzzy topological spaces and investigate the equivalent conditions of 𝑞𝛼𝑟- pre-continuity.
Highlights
Šostak [28] defined I-fuzzy topology as an extension of Chang’s fuzzy topology [2]
Ramadan [23] gave a similar definition of fuzzy topology on a fuzzy set in Šostak’s sense and called by the name "smooth fuzzy topological space"
On the other hand, studying different forms of continuous functions in topological space is an interesting area of research which attracts many researchers
Summary
In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτr-closure, Rτr-interior, etc., and present all possible relations among these types of continuities.
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