Behavioral analysis of aggregation in multicriteria decision aid

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to the weighted arithmetic mean has to be adopted. It was shown that, under rather natural conditions, the discrete Choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by the taking into consideration of the interaction among criteria. However, since this operator is constructed from coefficients (weights) whose meaning is not always very clear for the decision maker, it is useful to define from these coefficients some indices that offer a better understanding of the behavioral properties of the aggregation. We present and discuss the following indices: the global importance of criteria, the interaction among criteria, the influence of the criteria on the aggregation, the tolerance of the decision maker, and the dispersion of the weights on the criteria.