Textures and Fuzzy Rough Sets

Authors:
Murat Diker
Affiliations:
(Correspd.) Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey. mdiker@hacettepe.edu.tr
Venue:
Fundamenta Informaticae - Advances in Rough Set Theory
Year:
2011

Citing 15
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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. (This work has been supported by the Turkish Scientific and Technological Research Council under the project TBAG 109T683.)