The Covering Upper Approximation by Subcovering

Rough set theory is a useful tool for data mining to deal with the vagueness and granularity in information systems. The study of covering-based rough sets has made an interesting contribution to the classical rough set theory. Reduction is one of the fundamental and significant concepts in covering-based rough sets. This paper studies covering-based rough sets from the standpoint of the subcovering. We define a type of covering upper approximation operation through subcoverings and present basic properties for this operation. Then we explore the relationship between reducible elements in a covering, one of the core concepts in covering-based rough sets, and this type of operation. It is interesting that the covering upper approximation operation defined from this standpoint is the same as the fifth type of covering upper approximation operation.