On fuzzy T1-topological spaces

Journal of Mathematical Analysis and Applications, 1984

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.

Journal of Mathematical Analysis and Applications, 1988

Journal of Mathematical Analysis and Applications, 1983

International Journal of Fuzzy Systems and Advanced Applications, 2021

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip’s approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip’s article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces

Journal of Mathematical Analysis and Applications, 1981

We introduce the notion of a fuzzy Hausdorff topological space and make a few observations to establish the appropriateness of this notion.

Fuzzy Sets and Systems, 1992

A new category for fuzzy topological spaces is defined that includes some important categories proposed so far. A new category for fuzzy sets is also proposed.

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

Fuzzy Sets and Systems, 1998

The concept of induced fuzzy topological space, introduced by Weiss [J. Math. Anal. Appl. 50 (1975) 142 150], was defined with the notions of a lower semi-continuous function.

2012

We introduce the concepts of generalized fuzzy topological spaces, generalized fuzzy neighborhood systems, in Sostak sense. Furthermore, we construct generalized fuzzy interior, generalized fuzzy closure on generalized fuzzy topological space and generalized fuzzy neighborhood system. Also, we introduce the concepts of generalized fuzzy () , y y ¢-continuous. We study their properties and discuss the relationships between these concepts.