On the topological structure of granular reducts with covering rough sets

Covering generalized rough set is a substantial extension to the traditional rough set. Coverings are naturally relevant to topologies. Reduction is one of the most important issues in covering rough set theory. Therefore, there is an endogenous relation between reducts of a covering and topologies. With both theoretical and practical significance, exploring the topological interdependency between coverings and its granular reducts raises the application of topological methods in data mining. In this study we find that the N-reducts of a covering are the minimal subbases of the induced topology. The correlations suggest several simplified granular reduction algorithms in covering rough sets.