Criteria Interactions in Multiple Criteria Decision Aiding: A Choquet Formulation for the TODIM Method

The problem of modeling interactions between criteria in Multiple Criteria Decision Aiding (MCDA) has been approached by a number of authors. That problem arises when there are visible redundancies and synergies among criteria. Aggregation models exist that have been conceived to take care of criteria interdependences. From these aggregation models a special attention has been given to the Choquet integral, and its possibilities and limitations have been pointed out. In this paper it is shown how measures of criteria interaction can be computed for the TODIM method of MCDA by using the Choquet integral. The key conclusions from this case study are listed below: (i) the use of the Choquet integral minimizes the calculations by TODIM since it is unnecessary to normalize the raw data; (ii) not only precise values can be used but also interval data; this second situation would lead to using a fuzzy triangular number; (iii) by using the Choquet integral more complex additive models can be used that allow for taking dependencies between criteria into consideration. As important elements of future research the authors plan to encompass in their analysis new concepts such as generalizations of Choquet integral and the bipolar Cumulative Prospect Theory.