scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Soft set theory—First results

01 Feb 1999-Computers & Mathematics With Applications (Pergamon)-Vol. 37, pp 19-31
TL;DR: The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the the theory, and to discuss some problems of the future.
Abstract: The soft set theory offers a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the theory, and to discuss some problems of the future.
Citations
More filters
Journal ArticleDOI
TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.
Abstract: In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

2,114 citations


Cites background or methods from "Soft set theory—First results"

  • ...Molodtsov [7] defined the soft set in the following way....

    [...]

  • ...But all these theories have their inherent difficulties as pointed out in [7]....

    [...]

  • ...Consequently, Molodtsov [7] initiated the concept of soft theory as a mathematical tool for dealing with uncertainties which is free from the above difficulties....

    [...]

  • ...By the suggestions given by Molodtsov in [7], we present the notion of AND and OR operations on two soft sets as below....

    [...]

  • ...) Soft set theory has a rich potential for applications in several directions, few of which had been shown by Molodtsov in his pioneer work [7]....

    [...]

Journal ArticleDOI
TL;DR: In this article, the theory of soft sets was applied to solve a decision-making problem using rough mathematics, and the results showed that soft sets can be used to solve decision making problems.
Abstract: In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.

1,491 citations

Journal ArticleDOI
TL;DR: This paper points out that several assertions in a previous paper by Maji et al. are not true in general, and gives some new notions such as the restricted intersection, the restricted union, therestricted difference and the extended intersection of two soft sets.
Abstract: Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. In this paper, we first point out that several assertions (Proposition 2.3 (iv)-(vi), Proposition 2.4 and Proposition 2.6 (iii), (iv)) in a previous paper by Maji et al. [P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555-562] are not true in general, by counterexamples. Furthermore, based on the analysis of several operations on soft sets introduced in the same paper, we give some new notions such as the restricted intersection, the restricted union, the restricted difference and the extended intersection of two soft sets. Moreover, we improve the notion of complement of a soft set, and prove that certain De Morgan's laws hold in soft set theory with respect to these new definitions.

1,223 citations


Cites background from "Soft set theory—First results"

  • ...Molodtsov [1] defined the notion of a soft set in the following way:...

    [...]

  • ...For illustration, Molodtsov considered several examples in [1]....

    [...]

Journal ArticleDOI
TL;DR: The basic properties of soft sets are introduced, and compare soft sets to the related concepts of fuzzy sets and rough sets, and a definition of soft groups is given.
Abstract: Molodtsov introduced the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. In this paper we introduce the basic properties of soft sets, and compare soft sets to the related concepts of fuzzy sets and rough sets. We then give a definition of soft groups, and derive their basic properties using Molodtsov's definition of the soft sets.

1,012 citations


Cites background from "Soft set theory—First results"

  • ...Most of these applications have already been demonstrated in Molodtsov’s book [13]....

    [...]

Journal ArticleDOI
TL;DR: It is shown that a soft topological space gives a parametrized family of topological spaces and it is established that the converse does not hold.
Abstract: 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.

832 citations

References
More filters
Book
31 Dec 1985

419 citations