More on Fuzzy Topological Spaces on Fuzzy Space

Journal of Bangladesh Academy of Sciences, 1970

We deal with fuzzy topology. In this paper, we introduce the concept of mixed fuzzy topology which is constructed from two fuzzy topologies on the same fuzzy set X and study several features of this mixed fuzzy topology. Keywords: Fuzzy Topological Spaces, Mixed fuzzy topology doi: 10.3329/jbas.v32i2.2433 Journal of Bangladesh Academy of Sciences Vol.32(2) 2008 142-150

Patan Prospective Journal

Fuzzy set was introduced by Zadeh in his classical paper of 1965. Three years later, Chang gave the definition of fuzzy topology, which is a family of fuzzy set satisfying the three classical axioms. In this paper, we have introduced and studied some new notions of To separation axioms in fuzzy topological spaces by using quasi-coincident relation for fuzzy set. Every ordinary (crisp) topological space vacuously satisfies condition of being quasi-To. In this paper concept of quasi coincident relation used to introduce and investigate some quasi separation axioms such as To, T1, & T2. Concerning quasi-To space in the general frame work of fuzzy topological spaces.

Advances in Pure Mathematics, 2021

Topology has enormous applications on fuzzy set. An attention can be brought to the mathematicians about these topological applications on fuzzy set by this article. In this research, first we have classified the fuzzy sets and topological spaces, and then we have made relation between elements of them. For expediency, with mathematical view few basic definitions about crisp set and fuzzy set have been recalled. Then we have discussed about topological spaces. Finally, in the last section, the fuzzy topological spaces which is our main object we have developed the relation between fuzzy sets and topological spaces. Moreover, this article has been concluded with the examination of some of its properties and certain relationships among the closure of these spaces.

Filomat

In this paper, a new form of separation axioms called r-fuzzy soft Ti;(i = 0,1,2,3,4), r-fuzzy soft regular and r-fuzzy soft normal axioms are introduced in a fuzzy soft topological space based on the paper Ayg?no?lu et al. [7]. Also, the relations of these axioms with each other are investigated with the help of examples. Furthermore, some fuzzy soft invariance properties, namely fuzzy soft topological property and hereditary property are specified.

Journal of Mathematical Analysis and Applications, 1987

A fuzzy topological analog of the R, separation axiom of topology is introduced and its appropriateness is established. 6? I987 Academic Press, Inc

In this paper, separation and regularity axioms in fuzzy topology on fuzzy set are defined and studied. We investigate some of its characterizations and discuss certain relationship among them with some necessary counterexamples. Moreover some of their basic properties are examined. In addition, goodness and hereditary properties are discussed.

2020

In this paper, we introduce two notions of property in fuzzy topological spaces by using quasi-coincidence sense and we establish relationship among our and others such notions. We also show that all these notations satisfy good extension property. Also hereditary, productive and projective properties are satisfied by these notions. We observe that all these concepts are preserved under one-one, onto, fuzzy open and fuzzy continuous mappings. Finally, we discuss initial and final fuzzy topologies on our second notion.

2018

In this paper, regularity and separation axioms in fuzzy soft topological spaces are defined and studied by using quasi-coincident relation and fuzzy soft neighborhood system. We discuss its charaterizations and relationship among them. In addition, goodness and hereditary properties are discussed.

The aim of this paper is to introduce the concept of fuzzy semi open and fuzzy semi closed sets of a fuzzy topological space. Some characterizations are discussed, examples are given and properties are established. Also, we define fuzzy semi interior and fuzzy semi closure operators. And we introduce fuzzy t-set, -SO extremely disconnected space analyse the relations between them. MSC 2010: 54A40, 03E72.

2019

Fuzzy soft separation axioms was introduced by Mahanta and Das ([5]) using the definitions of a `fuzzy soft point' and `the complement of a fuzzy soft point is a fuzzy soft point', and `distinct of fuzzy soft points' in there sense. In this paper we, introduce fuzzy soft separation axioms in terms of the modified definitions of a `fuzzy soft point', the complement of a fuzzy soft point is a fuzzy soft set' and `distinct of fuzzy soft points'([7]). Also, we study some of their properties. Finally, we discuss fuzzy soft topological property for such spaces.