In the context of Multiple Criteria Decision Making, this paper studies the robustness of the sign of nonadditivity index for subset of criteria in a Choquet integral model. In the case where the set of alternatives is discrete, the use of the nonadditivity index proposed in the literature often leads to interpretations which are not always robust. Indeed, the sign of this nonadditivity index can depend on the arbitrary choice of a numerical representation in the set of all numerical representations compatible with the ordinal preferential information given by the Decision Maker. We characterize the ordinal preferential information for which the problem appears. We also propose a linear program allowing to test the non robustness of the sign of nonadditivity index for subset of criteria.

We deal with online learning of acyclic Conditional Preference networks (CP-nets) from data streams, possibly corrupted with noise. We introduce a new, efficient algorithm relying on (i) information-theoretic measures defined over the induced preference rules, which allow us to deal with corrupted data in a principled way, and on (ii) the Hoeffding bound to define an asymptotically optimal decision criterion for selecting the best conditioned variable to update the learned network. This is the first algorithm dealing with online learning of CP-nets in the presence of noise. We provide a thorough theoretical analysis of the algorithm, and demonstrate its effectiveness through an empirical evaluation on synthetic and on real datasets.