Robust Ordinal Regression for Dominance-based Rough Set Approach to multiple criteria sorting

We present a new multiple criteria sorting method deriving from Dominance-based Rough Set Approach (DRSA). The preference information supplied by the Decision Maker (DM) is a set of possibly imprecise and inconsistent assignment examples on a subset of reference alternatives relatively well-known to the DM. To structure the data we use DRSA, and subsequently, represent the assignment examples by all minimal sets of rules covering all alternatives from the lower approximations of class unions. Such a set of rules is called minimal-cover set - it is one of the instances of the preference model compatible with DM's preference information. In this way, we implement the principle of Robust Ordinal Regression (ROR) to decision rule preference model. For each alternative, we derive the necessary and possible assignments specifying the range of classes to which the alternative is assigned by all or at least one compatible set of rules, respectively, as well as class acceptability indices. We also introduce the notion of a representative compatible minimal-cover set of rules whose selection builds on the results of ROR, addressing the robustness concern. Application of the approach is demonstrated by classifying 69 land zones in 4 classes representing different risk levels.