Relationship between generalized rough sets based on binary relation and covering
Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper systematically studies a type of generalized rough sets based on covering and the relationship between this type of covering-based rough sets and the generalized rough sets based on binary relation. Firstly, we present basic concepts and properties of this kind of rough sets. Then we investigate the relationships between this type of generalized rough sets and other five types of covering-based rough sets. The major contribution in this paper is that we establish the equivalency between this type of covering-based rough sets and a type of binary relation based rough sets. Through existing results in binary relation based rough sets, we present axiomatic systems for this type of covering-based lower and upper approximation operations. In addition, we explore the relationships among several important concepts such as minimal description, reduction, representative covering, exact covering, and unary covering in covering-based rough sets. Investigation of this type of covering-based will benefit to our understanding of other types of rough sets based on covering and binary relation.
rough set covering approximation reduction fuzzy set granular computing data mining