Abstract
Topological concepts and methods have been applied as useful tools to study computer science, information systems and rough set. Rough set was introduced by Pawlak. Its core concept is upper and lower approximation operations, which are the operations induced by an equivalent relation on a domain. They can also be seen as a closure operator and a interior operator of the topology induced by an equivalent relation on a domain. This paper explores rough set theory from the point of view of topology. I generalize the notions of rough sets based on the topological space. The set approximations are defined by using the new topological notions namely I-J-nearly open sets. The topological properties of the present approximations are introduced and compared to the previous one and shown to be more general.