Topological Approaches to the First Type of Covering-Based Rough Sets

Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper studies covering-based rough sets from the topological view. We explore the relationship between the relative closure and the first type of covering upper approximation. The major contributions of this paper are that we use the definition of the relative closure and the relative interior to discuss the conditions under which the relative operators satisfy certain classical properties. The theorems we get generalize some of the results in Zhu's paper.