Rough set theory has proved to be a useful tool for rule induction. But, the theory based on indiscernibility relation or similarity relation cannot induce rules from decision tables with criteria. Greco et al have proposed a new rough set approach based on dominance relation to handle the problems. In this paper, the concept of dominance matrix is put forward and the dominance function is constructed to compute the minimal decision rules that are more general and applicable than the ones induced by the classical rough set theory. In addition, the methodology of simplification is presented to eliminate the redundancy in the rule set.