Variable consistency dominance-based rough set approach to preference learning in multicriteria ranking

We present a methodology for non-statistical preference learning in multicriteria ranking based on Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). A finite set of objects to be ranked is evaluated by a set of criteria, which are real-valued functions with ordinal or cardinal scales. Given the statement of a multicriteria ranking problem, the only objective information one can get is the dominance relation over the set of objects. The dominance relation is, however, too poor because it leaves many objects incomparable. To enrich this relation, and make the objects more comparable, a decision maker (DM) must supply some preference information revealing her/his value system with respect to multicriteria evaluations. We are considering a frequent case, when the preference information has the form of pairwise comparisons of some objects relatively well known to the DM, called reference objects. This information is thus composed of some decision examples on the reference objects. It is the input data for a method that learns the preferences of the DM. Since this information is prone to inconsistencies, we propose to structure it using VC-DRSA. Then, the pairs of objects that are sufficiently consistent serve as a basis for induction of a preference model. This model has the form of a set of “if …, then …” decision rules. Application of these rules on the whole set of objects to be ranked yields a fuzzy preference structure (directed weighted graph). This preference structure is then exploited using a ranking method, so as to work out a final recommendation. We propose a list of properties that helps to choose a proper ranking method. The methodology is illustrated by an example.