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

Abstract

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 second 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.

Topological structures of a type of granule based covering rough sets

“…Zhao constructed a topology in a covering approximation space and explored topological properties of the topological space [45]. Chen and Li defined open sets, closed sets, rough inclusion, rough equality on covering rough sets and studied some of their properties [7][8][9]. Ge, Bai, Yun, Bian and Wang gave topological characterizations of the covering C for covering upper approximation operators to be closure operators [2,12].…”