The fourth type of covering-based rough sets

As a technique for granular computing, rough sets deal with the vagueness and granularity in information systems. Covering-based rough sets have been proposed to generalize this theory for wider application. Three types of covering-based rough sets have been studied for different situations. To make the theory more complete, this paper proposes a fourth type of covering-based rough sets. Compared with the existing ones, the new type shows its special characteristic in the interdependency between its lower and upper approximations. We carry out a systematical study of this new theory. First, we discuss basic properties such as normality, contraction, and monotone. Then we investigate the conditions for this type of covering-based rough sets to satisfy the properties of Pawlak’s rough sets and study the interdependency between the lower and upper approximation operations. In addition, axiomatic systems for the lower and upper approximation operations are established. Lastly, we address the relationships between this type of covering-based rough sets and the three existing ones.