Textural approach to generalized rough sets based on relations

Diker, Murat

doi:10.1016/j.ins.2009.11.032

Cited by 32 publications

(18 citation statements)

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“…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.…”

Section: Introductionmentioning

confidence: 91%

“…A direlation (r, R) on a texture (U, U) gives us an i-c * space where r ← is an interior operator and R ← is a closure operator on (U, U) [8] and hence, we may note that (U, U, r ← , R ← ) is an i-c* space, and (U, U, r, R) is called direlational i-c * space. In fact, every complemented i-c* space corresponds to a textural rough set system which is studied in [8], and so (U, U, σ, r, R) is called direlational approximation space if (r, R) is complemented.…”

Section: Please Scroll Down For Articlementioning

confidence: 99%

“…In fact, every complemented i-c* space corresponds to a textural rough set system which is studied in [8], and so (U, U, σ, r, R) is called direlational approximation space if (r, R) is complemented. Direlational i-c* spaces and bicontinuous difunctions form a category denoted by dfIC* dr .…”

Section: Please Scroll Down For Articlementioning

confidence: 99%

“…In [12], any two set valued mappings int, cl : U → U are said to be generalized interior and closure operators respectively, and the quadruple (U, U, int, cl) is called to be a generalized interior-closure space (gic-space). Also, the textural lower-upper approximation operators which are defined by Diker [8], are set valued mappings. Hence, textural approximation operators may be considered a complemented gicspace.…”

Section: Is Called Bicontinuous If It Is Both Continuous and Cocontinmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 91%

Section: Please Scroll Down For Articlementioning

confidence: 99%

Section: Please Scroll Down For Articlementioning

confidence: 99%

Section: Is Called Bicontinuous If It Is Both Continuous and Cocontinmentioning

confidence: 99%

See 2 more Smart Citations

A categorical view of textural approximation spaces

Dost

2015

Quaestiones Mathematicae

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“…That is, the equivalence relation on the universe limits the theory's application to a certain extent because incomplete information systems and real-valued information systems are the main research topics in the area of knowledge representation. To address this issue, generalizations of the rough set theory have been considered by scholars to address complex practical problems [6,8,25,28,32,34,38].…”

Section: Introductionmentioning

confidence: 99%