On the Relationship Between the Algebra View and Information View of Rough Set Theory

Rough set is a valid mathematical theory developed in recent years, which has the ability to deal with imprecise, uncertain, and vague information. It has been applied in such fields as machine learning, data mining, intelligent data analyzing and control algorithm acquiring successfully. In this paper, we will study the relationship between the algebra view and information view of rough set theory. The equivalent relationship between the algebra view and information view of rough set theory in consistent information systems is analyzed and the inequivalent relationship between these two views in inconsistent information systems are discovered. It corrects an error of many researchers, that is, the algebra view and information view of rough set are equivalent.