On some new operations in soft set theory
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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.
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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.
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Citations
On fuzzy soft intra-regular Abel–Grassmann’s groupoids
Asad Ali,Madad Khan,Fu-Gui Shi +2 more
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TL;DR: In this article, the structural properties of an intra-regular groupoid were characterized using the properties of fuzzy soft sets and soft right ideals, and the authors introduced and used the concept of ''fuzzy soft sets'' and ''soft right ideals''.
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Soft W Hausdorff Spaces
TL;DR: In this paper, the concept of WHausdorffness in soft topological spaces is introduced by referring the definition of Fuzzy Hausdorfness introduced by Warren, R.H.
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A new perspective on soft topology
Mustafa Burç Kandemir
- 06 Apr 2018
TL;DR: Some basic topological concepts such as Hausdorffness, compactness, connectedness for soft topological spaces and study their some properties.
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Fibrewise soft ideal topological space
Y. Y. Yousif,Mohammed A H Ghafel +1 more
- 01 May 2018
Abstract: In this work we explain and discuss new notion of fibrewise topological spaces, called fibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.
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Rough Soft Sets in Fuzzy Setting
Xueyou Chen
- 12 Jun 2013
TL;DR: The notion of a soft set in L-set theory is defined, several operators for L- soft set theory are introduced, and the rough operators on the set of all L-soft sets induced by the rough operator on L X are investigated.
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References
Soft set theory—First results
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.
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Soft set theory
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.
2.5K
Soft sets and soft groups
Hacı Aktaş,Naim Çağman +1 more
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.
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Soft semirings
TL;DR: This paper initiates the study of soft semirings by using the soft set theory, and the notions of soft Semirings, soft subsemirings,soft ideals, idealistic softSemirings and soft semiring homomorphisms are introduced, and several related properties are investigated.
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A note on Soft Set Theory [Comput. Math. Appl. 45 (4-5) (2003) 555-562]
TL;DR: It is pointed out that the assertion of Maji, Biswas and Roy that (F,A,A)@?@? @?@F=@F, is incorrect by a counterexample.