Chandran Kalaivani, Rajakumar Roopkumar


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 ๐‘…๐œ๐‘Ÿ-closure, ๐‘…๐œ๐‘Ÿ-interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of ฮฑ-quasi-coincidence, ๐‘ž๐›ผ๐‘Ÿ-pre-neighborhood, ๐‘ž๐›ผ๐‘Ÿ-pre-clo-sure and ๐‘ž๐›ผ๐‘Ÿ- pre-continuous function in smooth fuzzy topological spaces and investigate the equivalent conditions of ๐‘ž๐›ผ๐‘Ÿ- pre-continuity.


fuzzy proper function; smooth fuzzy topology; smooth fuzzy continuity; fuzzy closure; fuzzy interior

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