Necessary and possible interaction between criteria in a 2-additive Choquet integral model

This paper deals with the interpretation of the 2-additive Choquet integral model in the context of Multiple Criteria Decision Making. When the set of alternatives is discrete, using classical interaction indices proposed in the literature may lead to interpretations that are not robust. Indeed, the sign of these indices may depend upon the arbitrary choice of a numerical representation within the set of all possible numerical representations. We tackle this problem in two ways. First, in the context of binary alternatives, we characterize the preference relations for which the problem does not occur. Outside the framework of binary alternatives, we propose a simple linear programming model allowing one to test for robust conclusions concerning the sign of interaction indices. We illustrate our results on a real world example in the domain of health.