In this paper, we introduce the notion of the $(\alpha ,\beta )$-weakly smooth fuzzy continuous proper function and discuss its properties. We also study several notions of connectedness in smooth fuzzy topological spaces and establish that the product of connected sets (spaces) is not connected in any sense, as well as investigate continuous images of smooth connected sets (spaces) under $(\alpha ,\beta )$-weakly smooth fuzzy continuous functions.

/pdf/some-results-on-fuzzy-proper-functions-and-connectedness-in-3n2w6knlsy.pdf

Some results on fuzzy proper functions and connectedness in smooth fuzzy topological spaces

Fuzzy Perfect Mappings and Q-Compactness in Smooth Fuzzy Topological Spaces

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 Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in smooth fuzzy topological spaces and investigate the equivalent conditions of qα r pre-continuity.

http://manu.edu.mk/contributions/NMBSci/Papers/2015_2_9_Kalaivani.pdf

Some weaker forms of smooth fuzzy continuous functions

The purpose of this paper is to introduce and study the concepts of fuzzy generalized pre-open sets, fuzzy generalized pre-closed sets and generalized pre-continuous fuzzy proper functions. Some of its properties have also been investigated. Relation between continuous fuzzy proper functions and generalized pre-continuous fuzzy proper functions has also been established.

On Generalized Pre-Continuous Fuzzy Proper Function from a Fuzzy Topological Space to Another Fuzzy Topological Space

The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of Sostak's I-fuzzy topological spaces are discussed. The projection maps are dened as fuzzy proper functions and their properties are proved.

Chandran Kalaivani

Papers

Continuity of fuzzy proper functions on sostak's i-fuzzy topological spaces

Some weaker forms of smooth fuzzy continuous functions