Abstract: Attribute reduction based on discernibility matrix is the most common methods in rough set attribute reduc- lion. Compared with discernibility matrix based on storage condition attribute,object matrix was defined in this paper. This object matrix uses the relationship between the decision value of the objects in tolerance class and condition attrib- ute,and what it stores is object set. hhen the definition of attribute reduction based on object matrix was given. It is proved that the attribute reduction acquired from this new method is ectuivalent to that based on positive region in in- complete information system. A heuristic algorithm for attribute reduction was presented which time complexity is max (()(I CI z I叽IIUI)，()(ICI))，and space complexity is()(ICI).An example was used to illustrate the feasi- bility of this new algorithm.

Key words: Discernibility matrix, Attribute reduction, Obj ect matrix, Positive region, Reduction algorithm