On compact and semicompact fuzzy soft topological spaces

In this Paper, we introduce a new definition of the cover so-called fuzzy soft p-cover. According to this notion, we define a new type of compactness in fuzzy soft topology so-called p *-compactness which is extension to Kandil's compactness in the fuzzy topology [7] and is avoid some Chang's deviations in the fuzzy and fuzzy soft topology [4]. Some of their basic results, properties and relations are investigated with some necessary examples.

2015

In this paper, union, and intersection of generalised fuzzy soft sets are introduced and some of their basic properties are studied. The objective of this paper is to introduce the generalised fuzzy soft topology over a soft universe with a fixed set of parameters. Generalised fuzzy soft points, generalised fuzzy soft closure, generalised fuzzy soft neighbourhood, generalised fuzzy soft interior, generalised fuzzy soft base are introduced and their basic properties are investigated. Finally, generalised fuzzy soft compact spaces are introduced and a few basic properties are taken up for consideration.

Hacettepe Journal of Mathematics and Statistics, 2015

The aim of this study is to define fuzzy soft topology which will be compatible to the fuzzy soft theory and investigate some of its fundamental properties. Firstly, we recall some basic properties of fuzzy soft sets and then we give the definitions of cartesian product of two fuzzy soft sets and projection mappings. Secondly, we introduce fuzzy soft topology and fuzzy soft continuous mapping. Moreover, we induce a fuzzy soft topology after given the definition of a fuzzy soft base. Also, we obtain an initial fuzzy soft topology and give the definition of product fuzzy soft topology. Finally, we prove that the category of fuzzy soft topological spaces FSTOP is a topological category over SET.

In this paper, we have studied some properties related to fuzzy soft topological spaces and some propositions have been established. Our work is an attempt to introduce the concepts on fuzzy soft point, fuzzy soft neighborhood, fuzzy soft closure, fuzzy soft interior, fuzzy soft subspace topology and thereby extend the work on fuzzy soft topological spaces.

2023

In this article, we apply the concept of fuzzy soft δ-open sets to defne new types of compactness in fuzzy soft topological spaces, namely, δ-compactness and δ *-compactness. We explore some of their basic properties and reveal the relationships between these types and that which are defned by other authors. Also, we show that δ *-compactness is more general than that which is presented in other papers. To clarify the obtained results and relationships, some illustrative examples are given.

2013

This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.

African Journal of Mathematics and Computer Science Research, 2018

In this manuscript, the concept of a generalized fuzzy soft point is introduced and some of its basic properties were studied. Also, the concepts of a generalized fuzzy soft base (subbase) and a generalized fuzzy soft subspace were introduced and some important theorems were established. Finally, the relationship between fuzzy soft set, intuitionistic fuzzy soft set, generalized fuzzy soft set and generalized intuitionistic fuzzy soft set were investigated.

Journal of Interdisciplinary Mathematics, 2021

Abstract In this article, we give the new concept of fuzzy w-supra soft topological spaces, fuzzy -supra soft topological spaces, also we introduced the fuzzy w-soft continuity (resp; fuzzy -supra soft topological spaces ) with supported by counter examples. Hence, we can see that all these concepts mean either implicitly the other or independent of one another. Finally, we introduce the notion of fuzzy w-supra soft compact (resp. fuzzy -supra soft topological spaces) spaces with relationship among them.

The main aim of this work is to provide a categorical framework for fuzzy soft topological spaces FST. We define some of their subcategories such as Top, STop, δ τ-FST, χ-FST, and α-FST. In general, we initiate some functors between them and discuss some results and relations of fuzzy soft maps. The relationships between FST and their subcategories are studied, for instance, we show that Top, STop are bireflective full subcategories of FST and α-FSTis a bicoreflective full subcategory of FST. Moreover, we demonstrate that Top, δ τ-FST, and χ-FST are isomorphic.

Journal of the Egyptian Mathematical Society, 2017

In this paper, we introduce some different types of fuzzy soft connected components related to the different types of fuzzy soft connectedness and based on an equivalence relation defined on the set of fuzzy soft points of X. We have investigated some very interesting properties for fuzzy soft connected components. We show that the fuzzy soft C 5-connected component may be not exists and if it exists, it may not be fuzzy soft closed set. Also, we introduced some very interesting properties for fuzzy soft connected components in discrete fuzzy soft topological spaces which is a departure from the general topology.