Notes on covering-based rough sets from topological point of view: Relationships with general framework of dual approximation operators

Abstract

In the recent article “On some types of covering rough sets from topological points of view” [14], the author develops a topological approach to covering-based rough sets. In this context, a number of corresponding approximation operators are introduced, their inclusion relationships are verified, and various conditions under which the operators coincide are proven.On the other hand, a lot of effort has recently been dedicated by several authors to study covering-based approximation operators within a general framework of dual approximation operators [2,3,7–10,12].In this note, we study correspondences between the framework of Zhao and the framework established in [2]. In particular, we evaluate how the newly introduced topological approximation operators relate to existing ones in terms of equalities and partial order relations.