On some new operations in soft set theory
TLDR
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.read more
Citations
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On soft topological spaces
Muhammad Shabir,Munazza Naz +1 more
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.
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Soft set theory and uni–int decision making
Naim Çağman,Serdar Enginoğlu +1 more
TL;DR: An uni-int decision making method which selects a set of optimum elements from the alternatives is constructed which shows that the method can be successfully applied to many problems that contain uncertainties.
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Soft sets combined with fuzzy sets and rough sets: a tentative approach
TL;DR: A possible fusion of fuzzy sets and rough sets is proposed to obtain a hybrid model called rough soft sets, based on a Pawlak approximation space, and a concept called soft–rough fuzzy sets is initiated, which extends Dubois and Prade's rough fuzzy sets.
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Picture fuzzy sets
TL;DR: The concept of picture fuzzy sets (PFS), which are direct extensions of the fuzzy sets and the intuitonistic fuzzy sets, are introduced and the basic preliminaries of PFS theory are presented.
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Soft matrix theory and its decision making
Naim Çağman,Serdar Enginoğlu +1 more
TL;DR: This work defines soft matrices and their operations which are more functional to make theoretical studies in the soft set theory and constructs a soft max-min decision making method which can be successfully applied to the problems that contain uncertainties.
References
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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.
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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.