In this article we are considering a multicriteria classification that differs from usual classification problems since it takes into account preference orders in the description of objects by condition and decision attributes. To deal with multicriteria classification we propose to use a dominance-based rough set approach (DRSA). This approach is different from the classic rough set approach (CRSA) because it takes into account preference orders in the domains of attributes and in the set of decision classes. Given a set of objects partitioned into pre-defined and preference-ordered classes, the new rough set approach is able to approximate this partition by means of dominance relations (instead of indiscernibility relations used in the CRSA). The rough approximation of this partition is a starting point for induction of if-then decision rules. The syntax of these rules is adapted to represent preference orders. The DRSA keeps the best properties of the CRSA: it analyses only facts present in data, and possible inconsistencies are not corrected. Moreover, the new approach does not need any prior discretization of continuous-valued attributes. In this article we characterize the DRSA as well as decision rules induced from these approximations. The usefulness of the DRSA and its advantages over the CRSA are presented in a real study of evaluation of the risk of business failure.