Rough reduction, in algebra view and information view

Rough set (RS) is a valid theory to deal with imprecise,, uncertain, and vague information. It has been applied successfully since it was developed by Professor Z. Pawlak in 1982 in such fields as machine learning, data mining, intelligent data analyzing, control algorithm acquiring, etc. The greatest advantage of the RS is its great ability to compute the reductions of information systems. Many researchers have done a lot of work in developing efficient algorithms to compute useful reductions of information systems. There also are some researchers working on the relationship between rough entropy and information entropy. They have developed some efficient reduction algorithms based on conditional information entropy. In this article, the relationship of the definitions of rough reduction in algebra view and information view is studied. Some relationships such as inclusion relationship under some conditions and equivalence relationship under some other conditions are presented. The inclusion relationship between the attribute importance defined in algebra view and information view is presented also. Some efficient heuristic reduction algorithms can be developed further using these results. (C) 2003 Wiley Periodicals, Inc.