On near soft sets

Filomat, 2017

Near set theory presents a fundamental basis for observation, comparison and classification of perceptual granules. Soft set theory is proposed as a general framework to model vagueness. The purpose of this paper is to combine these two theories in what are known near soft sets in defining near soft topology based on a nearness approximation space.

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2020

Near soft sets are considered as mathematical tools for dealing with ambiguities. In this study, we describe the near soft connectedness in near soft topological spaces, and introduce its concerned properties. Near soft sets are considered as mathematical tools for dealing with ambiguities. In this study, we describe the near soft connectedness in near soft topological spaces, and introduce its concerned properties. Near soft sets are considered as mathematical tools for dealing with ambiguities. In this study, we describe the near soft connectedness in near soft topological spaces, and introduce its concerned properties.

Kyungpook mathematical journal, 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi interior and semi closure of a soft set in a soft topological space. Various forms of soft functions, like semicontinuous, irresolute, semiopen soft functions are introduced and characterized. Further soft semicompactness, soft semiconnectedness and soft semiseparation axioms are introduced and studied.

2017

The main objective of this paper is to introduce and define a new class of sets called soft -open sets in soft topological spaces, which is subclass of soft pre-open sets. Several properties of this kind of sets are obtained. By using this soft set we present and study the concept of soft -continuous functions.

Journal of Applied Mathematics, Statistics and Informatics, 2020

In this paper, we have established topological soft sets over generalized topological spaces and topological spaces, and studied its structural properties. We have derived a topological soft set in any given topological space, and from this point of view, we have given necessary and sufficient condition for homeomorphic Alexandroff spaces using topological soft set technique. At last, we have derived a topological soft set using closed sets in any topological space and we have given necessary and sufficient condition for arbitrary homeomorphic topological spaces using them.

Science journal of University of Zakho, 2019

The objective of studing the current paper is to introduced a new class of soft open sets in soft topological spaces called soft "-open sets. Then soft "-open sets are used to study some soft topological concepts. Furthermore, the concept of soft "-continuous and almost soft "-continuous functions are defined by using the soft "-open sets. Some properties and Characterizations of such functions are given.

2019

Soft set theory is a useful mathematical tool to deal with uncertainty in a parametric manner. Near sets have been used as a tool to study extensions of topological spaces. The present paper introduces and studies nearness of finite order, SSnn − merotopy, in soft set theory. An SSmm − merotopic space (UU, ζζmm ,EE) is introduced for a given SSnn − merotopic space (UU, ζζ,EE), where mm and nn are integers with the restriction that 2 ≤ mm ≤ nn. For mm ≤ nn an SSnn − merotopy ζζ∗ from a given SSnn − merotopy ζζ having the property that ζζ = (ζζ∗)mm is constructed and the largest SSnn − merotopy having such property is derived. For an SSnn − merotopic space (UU, ζζ), every maximal ζζ − compatible family is a maximal ζζ − clan. Key-Words: Soft set; Grill operator; Soft Čech closure operator; Proximity spaces; Merotopic spaces.

Iraqi Journal of Science, 2020

In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Ƅc-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Ƅ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets.

Computers & Mathematics with Applications, 2011

In the present paper we introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft T i-spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft T 1-space is also presented.

Wasit journal for pure sciences, 2024

In the context of soft classes, Athar Kharal and B. Ahmad [6] defined a soft mapping and investigated some characteristics of soft set images and inverse images. The references ([7], [8] [9], [10], [11], [12], [13]) introduced and ABSTRACT: This paper introduces novel concepts of soft functions known as soft-irresolute, soft-open, and soft-closed function as well as some of their properties. The interrelationships of this newly defined soft functions with other types of soft functions are investigated, and the behaviors of soft-irresolute (respectively, soft-open, and soft-closed) functions under soft composition are studied. Finally, using soft-open sets, the concepts of soft-Hausdorff space are introduced and investigated.