On Some Structural Properties of Fuzzy Soft Topological Spaces

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.

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.

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.

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.

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.

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.

Computers & Mathematics With Applications, 2011

In this paper, the concept of fuzzy soft topology is introduced and some of its structural properties such as neighborhood of a fuzzy soft set, interior fuzzy soft set, fuzzy soft basis, fuzzy soft subspace topology are studied.

2015

In the present paper, we continue the study on fuzzy soft topological spaces and investigate the properties of fuzzy soft pre connected sets, fuzzy soft pre separated sets and fuzzy soft pre s-connected sets and have established several interesting properties supported by examples. Moreover, we show that a fuzzy soft pre disconnectedness property is not hereditary property in general. Since the authors introduced topological structures on fuzzy soft sets (7, 15, 44), so the pre topological properties, which introduced by Mahanta et al.(30), is generalized here to the fuzzy soft sets, which we hope to be useful in the fuzzy systems.

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.