Relational Perspectives on Covering Based Rough Approximation Operators

Generalized rough set models based on arbitrary binary relation and covering are two meaningful extensions of Pawlak´s rough set, and their relationship is an important and interesting issue. Any covering can induce two binary relations, one being a tolerance and the other being the specialization preorder. In this paper, four pairs of covering based rough upper and lower approximation operators are proved to be precisely Cech quasi-discrete closure and interior operators corresponding to the induced tolerance and specialization preordering, respectively. Axiomatic characterizations of these four types of covering rough upper (dually, lower) approximation operators are also discussed.