Textural approach to generalized rough sets based on relations |
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Authors: | Murat Diker |
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Affiliation: | Hacettepe University, Department of Mathematics, 06532 Beytepe, Ankara, Turkey |
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Abstract: | This paper presents a discussion on rough set theory from the textural point of view. A texturing is a family of subsets of a given universal set U satisfying certain conditions which are generally basic properties of the power set. The suitable morphisms between texture spaces are given by direlations defined as pairs (r,R) where r is a relation and R is a corelation. It is observed that the presections are natural generalizations for rough sets; more precisely, if (r,R) is a complemented direlation, then the inverse of the relation r (the corelation R) is actually a lower approximation operator (an upper approximation operator). |
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Keywords: | Direlation Dual operator Lower approximation Presection Relation Rough set Rough set algebra Texture Textural rough set algebra Upper approximation |
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