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The Choquet integral is a preference model used in Multiple Criteria DecisionAiding (MCDA) to deal with interactions between criteria. The StochasticMultiobjective Acceptability Analysis (SMAA) is an MCDA methodology used totake into account imprecision or lack of data in the problem at hand. Forexample, SMAA permits to compute the frequency that an alternative takes thek-th rank in the whole space of the admissible preference parameters, e.g. incase evaluations on the considered criteria are aggregated through the weightedsum model, in the space of weights compatible with the preference informationsupplied by the Decision Maker (DM). In this paper, we propose to integrate theSMAA methodology with the Choquet integral preference model in order to getrobust recommendations taking into account the whole space of preferenceparameters compatible with the DM's preference information. In case thealternatives are evaluated by all the criteria on a common scale, thepreference parameters are given by the capacity expressing the non-additiveweights, representing the importance of criteria and their interaction. If thecriteria are instead evaluated on different scales, besides the capacity,preference parameters include the common scale on which the evaluations ofcriteria have to be recoded to be compared. Our approach permits to explore thewhole space of preference parameters being capacities and common scalescompatible with the DM's preference information.

Stochastic Multiobjective Acceptability Analysis for the Choquet integral preference model and the scale construction problem