Putting Dominance-based Rough Set Approach and robust ordinal regression together

We propose to apply the Dominance-based Rough Set Approach (DRSA) on the results of multiple criteria decision aiding (MCDA) methods, in order to explain their recommendations in terms of rules involving conditions on evaluation criteria. The rules represent a decision model which is transparent and easy to interpret for the DM. In fact, decision rules give arguments to justify and explain the decision and, in a learning perspective, they can be the starting point for an interactive procedure for analyzing and constructing the DM's preferences. It enables his/her understanding of the conditions for the suggested recommendation, and provides useful information about the role of particular criteria or their subsets. DRSA can be used in junction with any MCDA method producing a classification result or a preference relation in the set of alternatives. In this paper, we apply DRSA to a recently proposed MCDA methodology, called Robust Ordinal Regression (ROR). The ROR approach to MCDA, also called disaggregation–aggregation approach, aims at inferring parameters of a preference model representing some holistic preference comparisons of alternatives provided by the decision maker (DM). Contrary to the usual ordinal regression approaches to MCDA, ROR takes into account the whole set of possible value of preference model parameters compatible with the DM's preference information, to work out a final recommendation. In consequence, ROR gives a recommendation in terms of necessary and possible consequences of the application of all the compatible sets of parameter values to the considered set of alternatives. UTAGMS and GRIP methods apply this approach, considering general monotonic additive value functions, and produce as a result the necessary and possible preference relations. In this paper we show how DRSA completes the decision aiding process started with ROR, providing a very useful interpretation of the preference relations in terms of decision rules.