Comparison research for attribution reduction based on information entropy and distribution consistent set

Rough set is a valid theory to deal with imprecise, uncertain, and vague information. For different aim in application, there are different definitions for the attribution reduction which were called attribution reduction based on positive region, information entropy, HU´s discernibility matrix and distribution consistent set, respectively. In this paper, the relationships of the attribute reductions based on information entropy and distribution consistent set are studied. A new conclusion is deduced that the attribute reduction based on information entropy is equal to that based on distribution consistent set.