Decision under uncertainty concerns acts characterized by outcomes that can be achieved with some probabilities. Recommending the best decisions is challenging because aggregation of the outcomes over probabilistic states of the world needs to respect preferences of decision makers (DMs). The method used to assist the DMs has to: rely on realistically available preference information, handle a possible inconsistency of this information, aggregate the outcomes in an intelligible and non-compensatory way. To respond satisfactorily to these requirements, we propose a methodology that relies on preference information in the form of decision examples provided by DMs on a subset of reference acts. As this information may be inconsistent with respect to stochastic dominance, it is structured using Dominance-based Rough Set Approach, and then used for inducing a preference model composed of "if..., then..." decision rules. Decision rules constitute an intelligible and non-compensatory aggregation model able to represent complex interactions. We induce all different minimal-cover sets of rules, each one being compatible with the consistent part of the preference information. Applying such compatible instances of the preference model on all considered acts, we get robust recommendations. We also present some indicators for judging the spaces of consensus and disagreement between DMs.
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