Quantile-constrained Choquet-Wasserstein p-box approximation of arbitrary belief functions

This paper considers the problem of approximating an arbitrary belief function in Dempster-Shafer theory, seen as the imprecise distribution of a random variable with finite range, with a suitable p-box. The quoted p-box is asked to minimize a Choquet-Wasserstein pseudo-distance while satisfying inequality constraints on the corresponding lower/upper quantile function. We show that the computation of the approximating p-box can be carried out efficiently through a generalization of the Dykstra’s algorithm by relying on a proper entropic formulation.