Covering-based approximation operators by boolean matrix

Covering-based rough approximation space is an important generalization of classical rough approximation space. Matrix is not only a classical field in mathematics, but also a powerful tool in computer science. Recently, boolean matrices have been employed to define the sixth type of covering-based approximation operators. In this paper, we use matrices to describe the other five types of approximation operators. These descriptions can be obtained via two types of boolean product operations. The equivalent descriptions of the first type of approximation operators with indiscernible neighborhood are studied. The fourth covering-based upper approximation operator is described by predecessor neighborhood, which is generated from a relation induced by a covering. These equivalent descriptions about the fourth and the first type of approximation operators are used to obtain the representations of these three approximation operators by matrices. This work provides a more general approach for covering-based approximations through matrix.