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Relationship between the algebra view and information view of rough set

Rough set is a valid mathematical theory developed in recent years. It 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 make a comparative study of the algebra view and information view of rough set theory. Some inequivalent relationships between these two views of rough set theory in inconsistent decision table systems are discovered. It corrects an error of many researchers, that is, the algebra view and information view of rough set theory are equivalent. It is helpful for developing heuristic knowledge reduction algorithms for inconsistent decision table systems.