Decision Rule Approach

In this chapter we present the methodology of Multiple-Criteria Decision Aiding (MCDA) based on preference modelling in terms of “if…, then …” decision rules. The basic assumption of the decision rule approach is that the decision maker (DM) accepts to give preference information in terms of examples of decisions and looks for simple rules justifying her decisions. An important advantage of this approach is the possibility of handling inconsistencies in the preference information, resulting from hesitations of the DM. The proposed methodology is based on the elementary, natural and rational principle of dominance. It says that if action x is at least as good as action y on each criterion from a considered family, then x is also comprehensively at least as good as y. The set of decision rules constituting the preference model is induced from the preference information using a knowledge discovery technique properly adapted in order to handle the dominance principle. The mathematical basis of the decision rule approach to MCDA is the Dominance-based Rough Set Approach (DRSA) developed by the authors. We present some basic applications of this approach, starting from multiple-criteria classification problems, and then going through decision under uncertainty, hierarchical decision making, classification problems with partially missing information, problems with imprecise information modelled by fuzzy sets, until multiple-criteria choice and ranking problems, and some classical problems of operations research. All these applications are illustrated by didactic examples whose aim is to show in an easy way how DRSA can be used in various contexts of MCDA.