A New Type of Covering Approximation Operators

Rough set theory is a useful tool for data mining. It is based on equivalence relations of a universe. The covering rough sets is an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. However, many basic notions in this theory are not as widely agreeable as in the Pawlak rough set theory. This paper investigates four types of covering rough sets for dealing with the vagueness and granularity in information systems. First, we compare some basic properties of approximation operations generated by a covering with those of the Pawlak´s rough sets. Then we mainly improve the definition of upper approximation for covering rough sets, and gain the fifth type of covering rough sets to make it more reasonable. Thus we set up a framework for the approximation operators of covering rough set, and getting more properties than the existing ones. Finally we study the inter dependency between the lower and upper approximation operations and relationships with five types of covering rough sets are discussed.