The refinement in covering-based rough sets

In the studies on covering-based rough sets, there are few discussions about the relation between a covering-element and objects in the covering-element. But it is actually a significant problem. In this paper, we give some better studies on the refinement of covering. Based on the refinement, some important concepts such as minimal description and neighborhood in covering-based rough sets are discussed. The properties of several coverings which generate the same refinement are studied as well. Finally, we compare the approximation sets of four models of covering-based rough sets before and after the refinement. The refinement can help us to better understand and study covering-based rough sets from a new viewpoint.