Mixed Semi-Pre 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

This paper describes the construction of a topological space from two different fuzzy topologies using the fuzzy b-q-nbd of a fuzzy point with respect to one topology and the fuzzy b-closure of a fuzzy set with respect to another topology. Additionally, some relationships are established between the two adopted topologies and the resulting mixed topology. Finally, we define countability on mixed fuzzy topological spaces and investigate the various quasi-type properties of such spaces.

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.

Journal of Mathematical Analysis and Applications, 1983

Rocky Mountain Journal of Mathematics, 1978

It is shown that fuzzy continuous functions can be characterized by the closure of fuzzy sets, a subbasis for a fuzzy topology and fuzzy neighborhoods. Additional results are obtained concerning the collection of all fuzzy topologies on a fixed set, the interior of a fuzzy set, the closure of a fuzzy set, a fuzzy limit point, the derived fuzzy set and the relative fuzzy topology.

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, 1997

The aim of this paper is to introduce and to study the concepts of induced fuzzy supra-topological spaces and s-lower semi-continuous functions, s-Lower semi-continuous functions turn out to be the natural tool for studying the induced fuzzy supra-topological spaces. © 1997 Elsevier Science Ltd.

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.

Neural Computing and Applications, 2012

In this paper, we give the concept of L-fuzzy Semi-Preopen operator in L-fuzzy topological spaces, and use them to score L-fuzzy SP-cmpactnness in L-fuzzy topological spaces. We also study the relationship between L-fuzzy SP-compactness and SP-compactness in L-topological spaces.

Soft Computing, 2012

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

Journal of Mathematical Analysis and Applications, 1988

2013

In this paper we introduce and study the notion of δ-continuity on mixed fuzzy topological spaces. We have investigated this notion in the light of the notion of q-neighbourhoods, q-coincidence, fuzzy δ-closure, fuzzy δ-interior. We have established the relationship between fuzzy continuity and fuzzy δ-continuity in mixed fuzzy topological spaces.

The aim of this paper to introduced a semi extremely disconnected space on Topological space in fuzzy sitting , Several properties and characterizations of such space are discussed. Key words :-fuzzy semi extremely disconnected space , fuzzy semi hyper connected space , Generalized fuzzy semi extremely disconnected space.

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.

Soft Computing, 2013

A new class of functions called L-fuzzy weakly Semi-Preopen (Semi-Preclosed) functions in Lfuzzy topological spaces are introduced in this paper. Some characterizations of this class and its properties and the relationship with other classes of functions between L-fuzzy topological spaces are also obtained.