Multi-criteria formulations with uncertain satisfactions

We discuss the role that the Choquet integral plays in the aggregation of criteria satisfaction in multi-criteria decision functions. We show how the choice of the associated measure allows for the formulation of many types of multi-criteria decision functions. We note that the need for an ordering of the criteria satisfactions causes difficulties in situations in which there exists a probabilistic type of uncertainty in the knowledge of the criteria satisfactions. We discuss an approach, called the probabilistic exceedance method, for allowing the aggregation of probabilistically satisfied criteria.