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.