Affiliations: Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey. [email protected]
Note: [] Address for correspondence: Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey This work has been supported by the Turkish Scientific and Technological Research Council under the project TBAG 109T683.
Abstract: In this paper, we consider the Alexandroff topology for texture spaces. We prove that there exists a one-to-one correspondence between the Alexandroff ditopologies, and the reflexive and transitive direlations on a given texture. Using textural fuzzy direlations on a fuzzy lattice, we obtain a fuzzy rough set algebra where the inverse fuzzy relation and inverse fuzzy corelation are the upper approximation and lower approximation, respectively. In a special case, this gives us the fuzzy rough sets which are calculated with respect to the min-t norm introduced by S. Gottwald, or the fuzzy rough sets which are considered by D. Pei.
Keywords: Alexandroff topology, approximation operator, direlation, fuzzy rough set algebra, rough set algebra, textural fuzzy direlation, textural rough set algebra, texture space
