  In multicriteria decision aiding (MCDA), the Choquet integral has been used
as an aggregation operator to deal with the case of interacting decision
criteria. While the application of the Choquet integral for ranking problems
have been receiving most of the attention, this paper rather focuses on
multicriteria sorting problems (MCSP). In the Choquet integral context, a
practical problem that arises is related to the elicitation of parameters known
as the Choquet capacities. We address the problem of Choquet capacity
identification for MCSP by applying the Stochastic Acceptability Multicriteri
Analysis (SMAA), proposing the SMAA-S-Choquet method. The proposed method is
also able to model uncertain data that may be present in both decision matrix
and limiting profiles, the latter a parameter associated with the sorting
problematic. We also introduce two new descriptive measures in order to conduct
reverse analysis regarding the capacities: the Scenario Acceptability Index and
the Scenario Central Capacity vector.
