A Comparison of Two Types of Covering-Based Rough Sets Through the Complement of Coverings

In recent years, many types of covering-based rough set models were established and the study of their relationships was a hot research topic. Covering-based rough sets defined by Zhu and ones defined by Xu and Zhang were compared with each other through binary relations. And the relationships between these two types were further explored by introducing a concept of complementary neighborhood. However, the essential connections between these two types have not been revealed. In this paper, we consider these two types of covering-based rough sets by introducing a notion of the complement of coverings. In fact, these two types are expressed by each other through the complement of coverings. Based on the above results, we analyze a notion of the extension of a covering, which is introduced on the basis of the complement of the covering. Finally, we further explore the structure of these types of covering-based rough set models. This study suggests some internal connections between covering-based rough sets and demonstrates a new research tendency of them.