Some Topological Properties of Covering Based Rough Sets

Covering based rough sets [3,15,16,17,18,19] have been introduced as an extension of the basic rough sets introduced by Pawlak [6]. There is only one way to define the lower approximation of a set using covering. However, as many as four definitions have been proposed for the upper approximation. Accordingly, four types of covering based rough sets have been defined. In this paper we introduced the general concept of kinds of covering based rough sets. Also, some topological properties involving the union and intersection of such sets have been established, which lead to determination of kinds of union and intersection of covering based rough sets. These properties can be used in the representation of distributed knowledge base systems.