Dominance-Based Rough Set Approach to Multiple Criteria Ranking with Sorting-Specific Preference Information

A novel multiple criteria decision aiding method is proposed, that delivers a recommendation characteristic for ranking problems but employs preference information typical for sorting problems. The method belongs to the category of ordinal regression methods: it starts with preference information provided by the Decision Maker (DM) in terms of decision examples, and then builds a preference model that reproduces these exemplary decisions. The ordinal regression is analogous to inductive learning of a model that is true in the closed world of data where it comes from. The sorting examples show an assignment of some alternatives to pre-defined and ordered quality classes. Although this preference information is purely ordinal, the number of quality classes separating two assigned alternatives is meaningful for an ordinal intensity of preference. Using an adaptation of the Dominance-based Rough Set Approach (DRSA), the method builds from this information a decision rule preference model. This model is then applied on a considered set of alternatives to finally rank them from the best to the worst. The decision rule preference model resulting from DRSA is able to represent the preference information about the ordinal intensity of preference without converting this information into a cardinal scale. Moreover, the decision rules can be interpreted straightforwardly by the DM, facilitating her understanding of the feedback between the preference information and the preference model. An illustrative case study performed in this paper supports this claim.