Abstract: Considered the inconsistent target information systems which respectively induce dominance relation on condition attribute set and ecauivalence relation on decision attribute set, Under this dominance-equivalence relation, the relationships were analyzed among three different reductions, compatible reduction maximum distribution reduction and positive domain reduction.The rule extraction method based on positive domain reduction(PDRIS) was improved by in troducing inferior relations together with dominance relations to extract rules with larger coverage. Finally, an example was given to illustrate our rule extraction method, and the experimental results on 13 UCI data were demonstrated to make comparisons between the proposed method and the PDRIS method.

Key words: Rough set, Dominance relation, Equivalence relation, Positive domain reduction, Rule extraction