Fuzzy Connectedness in Fuzzy Quad Topological Space

Patan prospective journal, 2023

Fuzzy sets were introduced by Zadeh in 1965, and three years later, Chang defined fuzzy topological spaces. Fuzzy topological spaces are families of fuzzy sets that satisfy the three classical axioms of topology. In this paper, we introduce and study some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. Every ordinary (crisp) topological space vacuously satisfies the condition of being quasi-To. We define the quasi-separation axioms for fuzzy topological spaces, as quasi-To, quasi-T1, Quasi-T2. We have introduced and studied some new notions of To separation axioms in fuzzy topological spaces using the quasicoincident relation for fuzzy sets. These quasi-separation axioms are weaker than the corresponding classical To separation axioms, but they are still useful for characterizing and studying fuzzy topological spaces.

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.

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.

Journal of Bangladesh Academy of Sciences, 2018

The aim of this paper is to study the fuzzy connectedness in Raja-Sethupathy-Lakshmivarahan's sense. Some characterizations and the properties of this type of fuzzy connectedness on fuzzy topological spaces are studied. Interrelationships among fuzzy connectedness are examined. We prove that fuzzy connectedness is preserved under fuzzy continuous mapping.

The purpose of this paper is to investigate some weaker forms of L-fuzzy connectedness notions, namely c 1 , c 2 , c 3 , c 4 and c s -connectedness in L-topological spaces. Also, we compare these concepts and find the interrelations between them.

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

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 ADVANCES IN MATHEMATICS

In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples.

International Journal of Pure and Applied Mathematics, 2019

We deal with fuzzy topology. In this paper, we introduce and study the notion of mixed -fuzzy on mixed fuzzy topological spaces. We have investigated this notion in the light of the notion of -q-neighbourhoods, -q-coincidence, fuzzy -closure, fuzzy -interior. Fur- ther, some relations are established between the two topologies used and their corresponding mixed fuzzy topological spaces.

Journal of Mathematical Analysis and Applications, 1984

Journal of Intelligent & Fuzzy Systems, 2017

Fuzzy soft topological space was introduced and studied by B. Tanay et al. [8]. This paper introduces fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space alongwith the study of fuzzy soft closure and fuzzy soft interior. Further, separation axioms and connectedness are introduced and investigated for fuzzy soft topological spaces.

The fundamental concept of a fuzzy set was introduced by L. A. Zadeh [111] in 1965 to provide a foundation for the development of many areas of knowledge. Consequently, this provides a natural frame work for generalizing many algebraic and topological concepts in various directions such as fuzzy groups, fuzzy rings, fuzzy vector spaces, fuzzy supra topology, fuzzy infra topology, fuzzy bitopology etc. many other branches of mathematics have been developed all over the world during the last five decades. In 1968, Chang [19] introduced the concepts of a fuzzy topological space by using the fuzzy set. Wong [105], Lowen[60], Hutton[48], Katsaras[52], Ali[3], Pu and Liu[72], etc., discussed various aspects of fuzzy topological spaces. Ying [74] introduced fuzzifying topology and developed this in a new direction with the semantic methods of continuous valued logic. In the frame work of

This paper deals with the concept of-limit points of crisp subsets of a fuzzy topological space and the concept of-closed sets in. A special type of crisp subsets (termed as-N-open sets) of a fuzzy topological space is defined as the complement of-closed sets in and a special class of ordinary topological spaces is introduced. This newly defined graded topological spaces (denoted by (N)) are used to study and characterize some fuzzy topological properties such as compactness and other compact-like covering properties and Hausdorffness, connectedness etc.

International Journal of Advanced Science and Engineering, 2023

The aim of this paper is to introduce a new class of Fuzzy sets, namely the wg**-closed fuzzy set for Fuzzy topological spaces. This new class properly lies between the class of closed Fuzzy set and the class of wg-closed fuzzy set, we also introduce the application of wg**-closed fuzzy sets, the concept of fuzzy wg**-connectedness in Fuzzy topological spaces, and their properties are obtained.