Group for Research in Decision Analysis

Generalized additive independence models and k-ary capacities in multicriteria decision making

Michel Grabisch Université Paris 1, France

In multiattribute utility theory (MAUT), the classical additive utility model assumes no interaction between criteria. So far, the two known ways to model interaction among criteria are the Choquet integral and the Generalized Additive Independence (GAI) model, introduced by Fishburn in 1967. Both are a generalization of additive utility, and the latter has flourished in the community of artificial intelligence mainly, supposing that attributes are discrete. The aim of the talk is to make a comparison between the two models. We will show that GAI models in the discrete case can be seen as a k-ary capacity, and the Choquet integral performs a parsimonious interpolation, yielding a continuous model. In a second part, we will show that 2-additive discrete GAI models can be decomposed into a sum of nonnegative terms, which considerably simplify optimization problems involving these models. This decomposition uses the vertices of the polytope of 2-additive k-ary capacities.

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