Rough set theory is one of the most important tools for data mining. The covering rough set (CRS) model is an excellent generalization of Pawlak rough sets. In this paper, we first investigate a number of basic properties of two types of CRS models. Especially, we study the operation properties of the two types of CRS models with respect to the unary covering. Meanwhile, several corresponding algorithms are constructed for computing the intersection and union of rough sets and some examples are employed to illustrate the effectiveness of these algorithms.Finally, as an application of the operation properties of CRS, some basic algebraic properties of CRS are explored. It is evident that these results will enrich the theory of covering rough sets.

The generalization of Pawlak rough sets is one of the most important directions of rough set theory. In this paper, we propose four types of multi-covering rough set (MCRS) models by combining multi-granulation rough sets with covering rough sets. In the first place, We propose two types of optimistic MCRS models and study their corresponding properties, and then propose another two types of the pessimistic MCRS models and study their corresponding properties as well. Finally, the relationships among the four types of MCRS and the interrelationships between the proposed MCRS models and the existing ones listed in [8] are further investigated.