Generalization of Pawlak’s rough approximation spaces by using δβ-open sets

The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of objects using an equivalence relation on the universe of his approximation space. This paper extends Pawlak’s rough set theory to a topological model where the set approximations are defined using the topological notion δβ-open sets. A number of important results using the topological notion δβ-open set are obtained. We also, proved that some of the properties of Pawlak’s rough set model are special instances of those of topological generalizations. Moreover, several important measures, related to the new model, such as accuracy measure and quality of approximation are presented.