Continuity of fuzzy proper functions on sostak's i-fuzzy topological spaces
30 Apr 2011-Communications of The Korean Mathematical Society (The Korean Mathematical Society)-Vol. 26, Iss: 2, pp 305-320
TL;DR: 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.
Abstract: 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.
Citations
More filters
01 Jan 2012
TL;DR: The notion of the $(\alpha,\beta )$-weakly smooth fuzzy continuous proper function is introduced and its properties are discussed and several notions of connectedness in smooth fuzzy topological spaces are studied.
Abstract: 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.
4 citations
TL;DR: It is pointed out that the product of two fuzzy closed sets of smooth fuzzy topological spaces need not be fuzzy closed with respect to the the existing notion of product Smooth fuzzy topology, and a new suitable product smooth fuzzyTopology is introduced to get this property.
3 citations
10 Apr 2017
TL;DR: This paper introduces various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, R τ -interior, etc., and presents all possible relations among these types of continuities.
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 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.
Cites background from "Continuity of fuzzy proper function..."
...The concepts of smooth fuzzy continuity, weakly smooth fuzzy continuity, qn-weakly smooth fuzzy continuity, (α,β)-weakly smooth fuzzy continuity of a fuzzy proper function on smooth fuzzy topological spaces and their inter-relations are investigated in [5, 23, 26, 27, 10]....
[...]
01 Jul 2019
TL;DR: The purpose of this paper is to introduce and study the concepts of fuzzy generalized pre-open sets, fuzzy generalizedpre-closed sets and generalizedPre-continuous fuzzy proper functions.
Abstract: 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.
References
More filters
1,997 citations
995 citations
"Continuity of fuzzy proper function..." refers background in this paper
...projection maps are defined as fuzzy proper functions and their properties are proved....
[...]
TL;DR: It will be shown in a following publication that contrary to the results obtained up to now, the Tychonoff-product theorem is safeguarded with fuzzy compactness.
894 citations
01 Jan 2001
TL;DR: In mathematics, certain notions of topology are also abstractions of classical concepts in the study of real or complex functions, including open sets, continuity, connectedness, compactness, and metric spaces.
Abstract: Topology has its roots in geometry and analysis. From a geometric point of view, topology was the study of properties preserved by a certain group of transformations, namely the homeomorphisms. Certain notions of topology are also abstractions of classical concepts in the study of real or complex functions. These concepts include open sets, continuity, connectedness, compactness, and metric spaces. They were a basic part of analysis before being generalized in topology.
473 citations