Algebras from Rough Sets

Banerjee, Mohua; Chakraborty, Mihir K.

doi:10.1007/978-3-642-18859-6_7

Cited by 70 publications

(24 citation statements)

References 21 publications

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“…There are many different interpretations of the notion of rough sets [3,20,32,41,51,53,55,57]. Similar to [28], we adopt the set-oriented interpretation of rough sets [20,28,30,32,36,46,47,51,52] and define a rough set as a pair of definable sets.…”

Section: A Fuzzy Set With Interval Values As Its Membership Values Ismentioning

confidence: 99%

Grey sets and greyness

Yang

John

2012

Information Sciences

109

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This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed.

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Section: A Fuzzy Set With Interval Values As Its Membership Values Ismentioning

confidence: 99%

Grey sets and greyness

Yang

John

2012

Information Sciences

109

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“…In some cases, only a fragment of logical studies connected with various rough set models is indicated in the literature [28,2,37,4,7,20,11,5,30,15,14,38,24,40,16,17,22] mostly from algebraic perspective. We shall work in the domain of covering-based rough sets.…”

Section: Introductionmentioning

confidence: 99%

Covering-based rough sets and modal logics. Part I

Chakraborty

2016

International Journal of Approximate Reasoning

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“…One can find a survey regarding the algebraic structures of R * in the case of an equivalence relation in [3]. The ordered structure of the generalized rough sets system was studied by Järvinen in [8].…”

Section: Introductionmentioning

confidence: 99%

On the Completion of Rough Sets System Determined by Arbitrary Binary Relations

Umadevi¹

2015

Fundamenta Informaticae

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In this paper, a solution is given to the problem proposed by Järvinen in [8]. A smallest completion of the rough sets system determined by an arbitrary binary relation is given. This completion, in the case of a quasi order, coincides with the rough sets system which is a Nelson algebra. Further, the algebraic properties of this completion has been studied.is a completion of (R * , ≤).In 1987, Gehrke and Walker [6] showed that the structure of the rough sets system determined by an equivalence relation R on U is isomorphic to 2 I × 3 J , where I = {R(x) | |R(x)| = 1} and J = {R(x) | |R(x)| > 1}. 2 I is the set of maps from I to a two element chain and 3 J is the set of maps from J to a three element chain. For reflexive relations R on U , the rough sets system determined by R can be order embed in (2 I × 3 J , ≤). Proposition 3.2. [8] If R is a reflexive relation on a set U , then (2 I ×3 J , ≤) is a completion of (R * , ≤), where I = {R(x) | |R(x)| = 1} and J = {R(x) | |R(x)| > 1}.

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Algebras from Rough Sets

Cited by 70 publications

References 21 publications

Grey sets and greyness

Grey sets and greyness

Covering-based rough sets and modal logics. Part I

On the Completion of Rough Sets System Determined by Arbitrary Binary Relations

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