Robust Ordinal Regression for dominance-based Rough Set Approach under uncertainty

We consider decision under uncertainty where preference information provided by a Decision Maker (DM) is a classification of some reference acts, relatively well-known to the DM, described by outcomes to be gained with given probabilities. We structure the classification data using a variant of the Dominance-based Rough Set Approach. Then, we induce from this data all possible minimal-cover sets of rules which correspond to all instances of the preference model compatible with the input preference information. We apply these instances on a set of unseen acts, and draw robust conclusions about their quality using the Robust Ordinal Regression paradigm. Specifically, for each act we derive the necessary and possible assignments specifying the range of classes to which the act is assigned by all or at least one compatible set of rules, respectively, as well as class acceptability indices. The whole approach is illustrated by a didactic example.