Textures and covering based rough sets

Diker, Murat; Uğur, Ayşegül Altay

doi:10.1016/j.ins.2011.08.012

Cited by 37 publications

(15 citation statements)

References 22 publications

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“…This theory can approximate subsets of universes by two definable subsets called lower and upper approximations and unravel knowledge hidden in information systems [8][9][10]14,[21][22][23][24][25][26][27][28][29][30][31][32]35,36,45,[55][56][57][58][59][60][61]. Another application of rough set theory is to reduce the number of attributes in databases.…”

Section: Introductionmentioning

confidence: 99%

Communication between information systems with covering based rough sets

Wang

Chen

Sun

et al. 2012

Information Sciences

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Section: Introductionmentioning

confidence: 99%

Communication between information systems with covering based rough sets

Wang

Chen

Sun

et al. 2012

Information Sciences

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“…Then C ′ = {(c U (B j ), c U (A j ) | j ∈ J} is a also dicover on (U, U). If C = C ′ , then (U, U, c U ) is called complemented dicovering space, and so c U (L C (A)) = H C (c U (A)), by [11,Theorem 9.2,Theorem 9.4]. Hence, (U, U, c U , L C , H C ) is a textural rough set algebra.…”

Section: Corollary 44 Let (I I) Be the Identity Direlation On (U U)mentioning

confidence: 99%

“…By [11,Theorem 8.2], the operators L C and H C satisfy (L 1 )-(L 2 ) and (H 1 )-(H 2 ). Hence, we have a direlation (r C , R C ) on (U, U), as in which (3.1), such that L C (A) = r ←…”

Section: A Morphism Is An Isomorphism If and Only If It Is Bijective mentioning

confidence: 99%

A categorical view of textural approximation spaces

Dost

2015

Quaestiones Mathematicae

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The basic motivation of the theory of textures is to find a convenient point-set based setting for fuzzy sets. Recent works on textures show that they also provide a useful model for rough set theory. In this paper, we show that i-c spaces (interior-closure texture spaces) can be regarded as a textural rough set systems on a single universe. Then we consider the approaches containing direlations and dicovers for textural rough sets and we give some basic results related to direlations and dicovers. Considering the discrete textures we discuss on these results for rough sets based on relations and coverings. Finally, we prove that the category of topological spaces and continuous functions is isomorphic to the category of (covering) approximation spaces and continuous functions. (2010): 54A40, 06A15, 18B30. Mathematics Subject Classification Introduction.Rough set theory is an extension of set theory as a mathematical approach to information systems represented by equivalence relations [15]. Generalizations of rough sets using arbitrary relations or coverings provide important real-life applications in natural computing [18][19][20][21].The starting point of the theory of textures is a point-set based setting for fuzzy sets [2,4]. Recent works on textures show that they also provide a useful model for rough set theory [8]. In this paper, we show that i-c spaces (interior-closure texture spaces) studied in [12, 13] can be regarded as a textural rough set systems on a single universe. Then we consider the approaches containing direlations and dicovers for textural rough sets and we give some basic results related to direlations and dicovers. Finally, considering the discrete textures we discuss on these results for rough sets based on relations and coverings.If interior and closure operators on a universe are grounded, isotonic, contractive (resp. expansive) and sublinear, then the universe with these operators is called an i-c space. Recall that i-c spaces (interior-closure texture spaces) and bicontinuous difunctions form a category denoted by dfIC [12]. Likewise, complemented ic spaces and bicontinuous complemented difunctions form a category denoted by cdfIC. Here, we work on i-c spaces which we call i-c * spaces whose interior and closure operators are grounded and sublinear where sublinearity holds for

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“…Ditopologies on textures unify the fuzzy topologies and classical topologies without the set complementation [6,7]. Recent works on textures show that they are also useful model for rough set theory [8] and semi-separation axioms [10]. On the other hand, it was given various types of completeness for diuniform texture spaces [13].…”

Section: Introductionmentioning

confidence: 99%

Completeness types for uniformity theory on textures

Yıldız

2015

Filomat

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Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a generalization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of classical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is presented a relation between dimetric texture spaces and quasi-pseudo metric spaces in the sense of J. F. Kelly.2010 MSC: 54E35; 54E40; 18B30; 54E15.

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Textures and covering based rough sets

Cited by 37 publications

References 22 publications

Communication between information systems with covering based rough sets

Communication between information systems with covering based rough sets

A categorical view of textural approximation spaces

Completeness types for uniformity theory on textures

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