Robustness analysis for decision under uncertainty with rule-based preference model

We consider decision under uncertainty as a multi-attribute classification problem where a set of acts is described by outcomes gained with given probabilities. The Decision Maker (DM) provides desired classification for a small subset of reference acts. Such preference information is structured using Dominance-based Rough Set Approach (DRSA), and the resulting lower approximations of the quality class unions are used as an input for construction of an aggregated preference model. We induce all minimal-cover sets of rules being compatible with the non-ambiguous assignment examples, and satisfying some additional requirements that may be imposed by the DM. Applying such compatible instances of the preference model on a set of all acts, we draw conclusions about the certainty of recommendation assured by different minimal-cover sets of rules. In particular, we analyze the diversity of class assignments, assignment-based preference relations, and class cardinalities. Then, we solve an optimization problem to get a univocal (precise) classification for all acts, taking into account the robustness concern. This optimization problem admits incorporation of additional indirect and imprecise preferences in form of desired class cardinalities and assignment-based pairwise comparisons. Finally, we extend the proposed approach to group decision under uncertainty. We present a set of indicators and outcomes for judging the spaces of consensus and disagreement between the DMs.