A categorical view of textural approximation spaces

Abstract

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.