Non-additive Robust Ordinal Regression with Choquet integral, Bipolar and Level Dependent Choquet integrals

Choquet integral has proved to be an effective aggregation model in multiple criteria decision analysis when interactions between criteria have to be taken into consideration. Recently, some generalizations of Choquet integral have been proposed to take into account more complex forms of interaction. This is the case of the bipolar Choquet integral and of the level dependent Choquet integral. To apply Choquet integral and its generalizations in decision problems it is necessary to determine one capacity permitting to represent the preferences of the Decision Maker (DM). In general the capacities are determined on the basis of some exemplary decisions supplied by the DM. It has been observed that effectively there is not only one capacity compatible with the DM’s preferences, but rather a whole set of capacities. The determination of the whole set of compatible capacities and the consequent definition of proper preference relations is the domain of the non-additive robust ordinal regression. The authors have already proposed a methodology for non-additive robust ordinal regression when dealing with classical Choquet integral in ranking or choice decision problems. In this presentation, we want to give the basis of a general methodology for non-additive robust ordinal regression for Choquet integral and its generalizations (therefore also the bipolar Choquet integral and the level dependent Choquet integral) in the whole spectrum of decision problems (i.e. not only ranking and choice, but also multicriteria classification). Keywords— Choquet integral; Bi-Capacity; Bipolar Choquet integral; Level dependent Choquet integral; Non-additive robust ordinal regression.