Categories of direlations and rough set approximation operators

Abstract

In this paper, we define a category R-APR whose objects are sets and morphisms are the pairs of rough set approximation operators. We show that R-APR is isomorphic to a full subcategory of the category cdrTex whose objects are complemented textures and morphisms are complemented direlations. Therefore, cdrTex may be regarded as an abstract model for the study of rough set theory. On the other hand, dagger symmetric monoidal categories play a central role in the abstract quantum mechanics. Here, we show that R-APR and cdrTex are also dagger symmetric monoidal categories. © 2010 Springer-Verlag Berlin Heidelberg.