  The Choquet integral is a preference model used in Multiple Criteria Decision
Aiding (MCDA) to deal with interactions between criteria. The Stochastic
Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology used to
take into account imprecision or lack of data in the problem at hand. For
example, SMAA permits to compute the frequency that an alternative takes the
k-th rank in the whole space of the admissible preference parameters, e.g. in
case evaluations on the considered criteria are aggregated through the weighted
sum model, in the space of weights compatible with the preference information
supplied by the Decision Maker (DM). In this paper, we propose to integrate the
SMAA methodology with the Choquet integral preference model in order to get
robust recommendations taking into account the whole space of preference
parameters compatible with the DM's preference information. In case the
alternatives are evaluated by all the criteria on a common scale, the
preference parameters are given by the capacity expressing the non-additive
weights, representing the importance of criteria and their interaction. If the
criteria are instead evaluated on different scales, besides the capacity,
preference parameters include the common scale on which the evaluations of
criteria have to be recoded to be compared. Our approach permits to explore the
whole space of preference parameters being capacities and common scales
compatible with the DM's preference information.
