Neighborhood operators for covering-based rough sets

Covering-based rough sets are important generalizations of the classical rough sets of Pawlak. A common way to shape lower and upper approximations within this framework is by means of a neighborhood operator. In this article, we study 24 such neighborhood operators that can be derived from a single covering. We verify equalities between them, reducing the original collection to 13 different neighborhood operators. For the latter, we establish a partial order, showing which operators yield smaller or greater neighborhoods than others.Six of the considered neighborhood operators result in new covering-based rough set approximation operators. We study how these new approximation operators relate to existing ones in terms of partial order relations, i.e., whether the generated approximations are in general greater, smaller or incomparable. Finally, we discuss the connection between the covering-based approximation operators and relation-based approximation operators, another prominent generalization of Pawlak’s rough sets.