Soft coverings and their parameter reductions

Li, Zhaowen; Xie, Ningxin; Wen, Guoqiu

doi:10.1016/j.asoc.2015.02.027

Cited by 45 publications

(16 citation statements)

References 26 publications

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“…In particular, Ali [2,3] proposed some novel operations and reduction of parameters on soft sets. Moreover, Li [26] studied soft covering and its parameter reduction. Recently, the algebraic structures of soft sets have been studied increasingly.…”

Section: Introductionmentioning

confidence: 99%

Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Ma¹,

Zhan²,

Davvaz³

2018

Filomat

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Let I be a normal hyperideal of a Krasner (m, n)-hyperring R, we define the relation ≡ I by x ≡ I y if and only if f (x, −y, (m−2) 0) ∩ I ∅, which is an equivalence relation on R. By means of this idea, we propose rough soft hyperrings (hyperideals) with respect to a normal hyperideal in a Krasner (m, n)-hyperring. Some lower and upper rough soft hyperideals with respect to a normal hyperideal are investigated, respectively. Further, we define the t-level set U(µ, t) = {(x, y) ∈ R × R| z∈ f (x,−y, (m−2) 0) µ(z) ≥ t} of a Krasner (m, n)-hyperring R and prove that it is an equivalence relation on R if µ is a fuzzy normal hyperideal of R. By means of this novel idea, we propose rough soft hyperideals by means of fuzzy normal hyperideals in Krasner (m, n)hyperrings. Finally, two novel kinds of decision making methods to rough soft Krasner (m, n)-hyperrings are established.

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Section: Introductionmentioning

confidence: 99%

Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Ma¹,

Zhan²,

Davvaz³

2018

Filomat

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“…Li et al [12] obtained the relationship among soft sets, soft rough sets and topologies. Li et al [13] studied parameter reductions of soft coverings.…”

Section: Introductionmentioning

confidence: 99%

Limits of <em>it</em>-Soft Sets and Their Applications for Rough Sets

Xie¹,

He²

2018

Preprint

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Soft set theory is a mathematical tool for dealing with uncertainty. This paper investigates limits of interval type of soft sets (for short, it-soft sets). The concept of it-soft sets is first introduced. Then, limits of it-soft sets are proposed and their properties are obtained. Next, point-wise continuity of it-soft sets and continuous it-soft sets are discussed. Finally, an application for rough sets is given.

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“…Li et al 13,14 considered roughness of fuzzy soft sets and obtained the relationship among soft sets, soft rough sets and topologies. Li et al 15 studied parameter reductions of soft coverings.…”

Section: Introductionmentioning

confidence: 99%

Soft points, s-relations and soft rough approximate operations

Yu¹

2017

IJCIS

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Soft set theory is a new mathematical tool to deal with uncertain problems. Since soft sets are defined by mappings and they lack "points", managing them is not convenient. In this paper, the concept of soft points is introduced and the relationship between soft points and soft sets is investigated. We prove that soft sets can be translated into soft point sets and may be expediently handled like ordinary sets. Moreover, we propose s-relations on soft sets. By means of soft points and these results, a pair of soft rough approximate operations is defined. Serial, reflexive, symmetric, transitive and Euclidean s-relations are characterized by using soft rough approximate operations. In addition, we research soft topologies induced by a reflexive s-relation on a special soft set and gives their structure.

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Soft coverings and their parameter reductions

Cited by 45 publications

References 26 publications

Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Applications of rough soft sets to Krasner (m,n)-hyperrings and corresponding decision making methods

Limits of <em>it</em>-Soft Sets and Their Applications for Rough Sets

Soft points, s-relations and soft rough approximate operations

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