ELECTRE methods with interaction between criteria: an extension of the concordance index

This paper presents an extension of the comprehensive (overall) concordance index of ELECTRE methods, which takes the interaction between criteria into account. In real-world decision-aiding situations, it is reasonable to consider only the interaction between a small number of criterion pairs. Three types of interaction have been considered: mutual strengthening, mutual weakening, and antagonistic. The new concordance index correctly takes into account such types of interactions, by imposing such conditions as boundary, monotonicity, and continuity. We demonstrate that the generalized index is able to take the three types of interaction, or dependencies, between criteria into account satisfactorily, first using quasi criteria and then using pseudo criteria. We also examine the links between the new concordance index and the Choquet integral.