A comparison of the GAI model and the Choquet integral w.r.t. a k-ary capacity

Abstract

This paper proposes a comparison between a GAI model and the Choquet integral w.r.t. a k-ary capacity. We show that these two models are much closer than one would expect. Based on this comparison, we show a new result on the GAI models: any 2-additive GAI model can be rewritten in such a way that all utility terms in the GAI decomposition are non-negative and monotone. This is very important in practice since it allows reducing the number of monotonicity constraints to be enforced in the elicitation process, from an exponential number (of the number of attributes) to a quadratic number.