Rough approximations based on different topologies via ideals

In this paper, we generalize the notations of rough sets based on the topological space. Firstly, we produce various topologies by using the concept of ideal, Cⱼ-neighbourhoods and Pⱼ-neighbourhoods. When we compare these topologies with previous topologies, we see that these topologies are more general. Then we introduce new methods to find the approximations by using these generated topologies. When we compare these methods with the previous methods, we see that these methods are more accurate.