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. Many researchers have studied rough sets in different view. In this paper, the algebra view and information view of rough set theory are analyzed and compared with each other systematically. Some equivalence relations and other kind of relations such as inclusion relations are resulted through comparing study. For example, the reduction under algebra view will be equivalent to the reduction under information view if the decision table is consistent. Otherwise, the reduction under information view will include the reduction under algebra view. These results will be useful for designing heuristic reduction algorithms.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.