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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.

Small Medium-sized Enterprises (SMEs) face many obstacles when they try to access credit market. These obstacles are increased if the SMEs are innovative. In this case, financial data are insufficient or even not reliable. Thus, when building a judgemental rating model, mainly based on qualitative criteria (soft information), it is very important to finance SMEs' activities. Until now, there isn't a multicriteria credit risk model based on soft information for innovative SMEs. In this paper, we try to fill this gap by presenting a multicriteria credit risk model, specifically, ELECTRE-TRI. To obtain robust SMEs' assignments to the risk classes, a SMAA-TRI analysis is also implemented. In fact, SMAA-TRI incorporates ELECTRE-TRI by considering different sets of preference parameters and uncertainty in the data via Monte Carlo simulations.Finally, we carry out a real case study, with the aim of illustrating the multicriteria credit risk model proposed.

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