Interpretation of multicriteria decision making models with interacting criteria

We consider general MCDA models with discrete attributes. These models are shown to be equivalent to a multichoice game and we put some emphasis on discrete Generalized Independence Models (GAI), especially those which are 2-additive, that is, limited to terms of at most two attributes. The chapter studies the interpretation of these models. For general MCDA models, we study how to define a meaningful importance index, and propose mainly two kinds on importance indices: the signed and the absolute importance indices. For 2-additive GAI models , we study the issue of the decomposition, which is not unique in general. We show that for a monotone 2-additive GAI model, it is always possible to obtain a decomposition where each term is monotone. This has important consequences on the tractability and interpretability of the model.