Interaction indices for multichoice games

Mustapha Ridaoui (1) , Michel Grabisch (1, 2) , Christophe Labreuche (3)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics
3 Thales Research and Technology [Palaiseau]

Models in Multicriteria Decision Analysis (MCDA) can be analyzed by means of an importance index and an interaction index for every group of criteria. We consider first discrete models in MCDA, without further restriction, which amounts to considering multichoice games, that is, cooperative games with several levels of participation. We propose and axiomatize two interaction indices for multichoice games: the signed interaction index and the absolute interaction index. In a second part, we consider the continuous case, supposing that the continuous model is obtained from a discrete one by means of the Choquet integral. We show that, as in the case of classical games, the interaction index defined for continuous aggre-gation functions coincides with the (signed) interaction index, up to a normalizing coefficient.

Mots clés: Choquet inte- gral; multicriteria decision analysis; interaction; multichoice game

Domaines: Economies et finances; Mathématique discrète [cs.DM]

Mustapha Ridaoui, Michel Grabisch, Christophe Labreuche. Interaction indices for multichoice games. Fuzzy Sets and Systems, 2020, 383, ⟨10.1016/j.fss.2019.04.008⟩. ⟨halshs-02380901⟩