Abstract
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.
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Notes
- 1.
The learning problem can be classically transformed into a linear program, where the training set is seen as linear constraints on the GAI variables (Bigot et al. 2012; Greco et al. 2014). It could also be possible to perform statistical learning, like in Tehrani et al. (2012), where the underlying optimization problem is a convex problem under linear constraints.
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Grabisch, M., Labreuche, C. (2019). Interpretation of Multicriteria Decision Making Models with Interacting Criteria. In: Doumpos, M., Figueira, J., Greco, S., Zopounidis, C. (eds) New Perspectives in Multiple Criteria Decision Making. Multiple Criteria Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-030-11482-4_6
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