On generalizing covering approximation space

In this paper, we present the covering rough sets based on neighborhoods by approximation operations as a new type of extended covering rough set models. In fact, we have introduced generalizations to W. Zhu approaches (Zhu, 2007). Based on the notion of neighborhood induced from any binary relation, four different pairs of dual approximation operators are defined with their properties being discussed. The relationships among these operators are investigated. Finally, an interesting theorem to generate different topologies is provided. Comparisons between these topologies are discussed. In addition, several examples and counter examples to indicate counter connections are investigated.