Aggregation of interacting criteria by means of the discrete Choquet integral

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. Under rather natural conditions, the discrete Choquet integral is proved to be an adequate aggregation operator that extends the weighted arithmetic mean by the taking into consideration of the interaction among criteria. The axiomatic that supports the Choquet integral is presented and some subfamilies are studied.