On Soft Separation Axioms via Fuzzy α-Open Soft Sets

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.

2017

In this paper, we introduce and investigate some weak soft separation axioms by using the notion of supra open soft sets, which is a generalization of the soft (resp. semi soft, pre soft, α-soft and β-soft separation axioms. We study the relationships between these new soft separation axioms and their relationships with some other properties.

gazi university journal of science, 2014

Arockiarani and Lancy (7), defined soft preopen (c losed) sets on soft topology. In this paper, we are continue investigating the properties of soft preopen (clos ed) sets and define soft preclosure and soft preinterior in soft topological spaces. We are also introduce and research basic properties of the concepts of soft prere gular spaces, soft P ₃�spaces, soft prenormal spaces and soft P ₄�spaces in soft topological spaces, which are basic for further research on soft topology and will fortify the footing of the theory of soft topological space.

Malaya Journal of Matematik,, 2019

The main objective of this article is to introduce soft generalized separation axioms in soft bi topological spaces relative to crisp points and soft points. Further we will address the behavior of soft semi T 3 and soft normal semi T 4 spaces at different angles with respect to ordinary points as well as with respect to soft points. Hereditary properties are also discussed. Keywords Soft sets, soft points,soft topology,soft bi topological space,soft semi open set, soft semi T i spaces(i=1,2,3,4), soft semi regular and soft semi normal spaces.

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.

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 new theory, 2017

this paper, a new class of generalized soft open sets in soft topological spaces, called soft e-open set is focused and investigated some properties of them. Then focused the relationships among soft δ-pre open sets, soft δ-semi open sets, soft pre-open sets and soft e-open sets. We also investigated the concepts of soft e-open functions, soft e-continuous, soft e-irresolute and soft e-homeomorphism on soft topological space and discussed their relations with existing soft continuous and other weaker forms of soft continuous functions. Further soft e-separation axioms have been introduced and investigated with the help of soft e-open sets. Finally, we observed that the collection Ser-h(X,τ,E) form a soft group.

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.

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.

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.