On Extreme Points of p-Boxes and Belief Functions

Ignacio Montes (1, 2, 3) , Sébastien Destercke (1, 2)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"
3 Universidad de Oviedo [Oviedo]

The extreme points of convex probability sets play an important practical role, especially for specific, easier to manipulate sets. Although this problem has been studied for many models (probability intervals, possibility distributions), it remains to be studied for imprecise cumulative distributions (a.k.a. p-boxes). This is what we do in this paper, where we characterize the maximal number of extreme points of a p-box, give a family of p-boxes that attains this number and show an algorithm that allows to compute the extreme points of a given p-box. To achieve all this, we also provide what we think to be a new characterization of extreme points of a belief function.

Domaines: Autre [cs.OH]

Ignacio Montes, Sébastien Destercke. On Extreme Points of p-Boxes and Belief Functions. 8th International Conference on Soft Methods in Probability and Statistics (SMPS 2016), Sep 2016, Rome, Italy. pp.363-371, ⟨10.1007/978-3-319-42972-4_45⟩. ⟨hal-01396198⟩