Bi-covering rough sets

Abstract

Rough set theory is a useful tool for knowledge discovery and data mining. Covering-based rough sets are important generalizations of the classical rough sets. Recently, the concept of the neighborhood has been applied to define different types of covering rough sets. In this paper, by introducing a new notion of the neighborhood known as bi-neighborhood, we consider four types of bi-neighborhoods related bi-covering rough sets. We first show some basic properties of the introduced bi-neighborhoods. We then explore the relationships between the considered bi-covering rough sets and investigate the properties of them. Also, we introduce and examine the properties of approximation operations generated by a bi-covering in comparison with those of Yao, Abd El-Monsef et. al  and the Pawlak's rough sets. Finally, figures are presented to show that the collection of all lower and upper approximations (bi-neighborhoods of all elements in the universe) introduced in this paper constructs a lattice in terms of the inclusion relation ⊆.