Characterizations and applications of parametric covering-based rough sets

Abstract

As a technique for granular computing, rough sets deal with the vagueness and granularity in information systems. Covering-based rough sets are natural extensions of the classical rough sets by relaxing the partitions to coverings and have been applied in many fields. However, many vital issues in covering-based rough sets, including attribute reduction, are NP-hard and therefore the algorithms for addressing them are usually greedy. Hence, it is necessary and helpful to generalize the covering-based rough sets from different viewpoints. In this paper, a new type of covering-based rough sets, named parametric covering-based rough sets, are proposed and some properties and applications of the parametric covering-based rough sets are investigated. First, a concept of inclusion degree is introduced into covering-based rough set theory to explore some properties of the parametric covering approximation space. Second, the parametric covering-based rough sets are established on the basis of inclusion degree. Moreover, some properties of the parametric covering-based rough sets are introduced. Third, it is found that the calculations of corresponding parametric covering-based lower and upper approximations can be converted into the operations of matrices, which makes the calculations convenient. Finally, a simple application of the parametric covering-based rough sets to network security is introduced.