Sändor Radeleczki

Jouni Järvinen, Sándor Radeleczki

We consider various types of algebras defined on the completion DM(RS) of the partially ordered set of rough sets induced by a reflexive relation. We restrict ourselves to the cases in which the completion forms a spatial and completely distributive lattice. We derive the conditions under which DM(RS) is a regular pseudocomplemented Kleene algebra and a completely distributive double Stone algebra. Finally, we describe reflexive relations for which DM(RS) has the same properties as in the case of an equivalence relation: it forms a completely distributive and spatial regular double Stone algebra.

Mani A, Sandor Radeleczki

In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and antisymmetric for a better behaved groupoidal semantics over the set of roughly equivalent objects by the first author. Another distinct algebraic semantics over the set of approximations, and a new knowledge interpretation are also invented in this research by her. Because of minimal conditions imposed on the relations, neighborhood granulations are used in the construction of all approximations (granular and pointwise). Necessary and sufficient conditions for the lattice of local upper approximations to be completely distributive are proved by the second author. These results are related to formal concept analysis. Applications to student centered learning and decision making are also outlined.