On the convex hull of k-additive 0-1 capacities and its application to model identification in decision making

The Choquet integral w.r.t. a capacity is versatile tool commonly used in decision making. Its practical identification requires, however, to solve an optimization problem with exponentially many variables and constraints. introduction of k-additive capacities, through the use Möbius transform, permits reduce number polynomial size, but leaves constraints exponential. When k=2, vertices set 2-additive capacities as polynomial. k>2, this solution no more applicable not known. We propose paper instead which are 0-1 valued. show that such polynomial, we observe loss generality very small for n=4, k=3, conjecture still holds larger values n. Also, study geometric properties convex hull valued capacities.