On characterizations of a pair of covering-based approximation operators

Granular computing is an emerging computing paradigm of information processing. Rough set theory is a kind of models of granular computing and is used to deal with the vagueness and granularity in information systems. Covering-based rough set theory is one of the most important extensions of the classical Pawlak rough set theory. In the covering-based rough set theory, the covering lower and upper approximation operators are two basic concepts. The axiomatic characterizations of covering-based approximation operators guarantee the existence of coverings reproducing the operators, so the rough set axiomatic system is the foundation of the covering-based rough set theory. In this paper, we present a new covering upper approximation operator and explore the basic properties of the covering upper approximation operator to find an axiomatic set for characterizing the covering upper approximation operator. We also discuss the relationships between the covering upper approximation operator and three other covering upper approximation operators, compare the covering upper approximation operator with the other covering upper approximation operators by defining precision degrees and rough degrees, and present the necessary and sufficient conditions for the covering upper approximation operators to be identical. The results not only are beneficial to enrich the kinds of the covering rough sets, but also have theoretical and actual significance to covering rough sets.