On extreme points of p-boxes and belief functions - Archive ouverte HAL Access content directly
Journal Articles Annals of Mathematics and Artificial Intelligence Year : 2017

On extreme points of p-boxes and belief functions

(1) , (1)
1

Abstract

Within imprecise probability theory, the extreme points of convex probability sets have an important practical role (to perform inference on graphical models, to compute expectation bounds,. . .). This is especially true for sets presenting specic features that make them easy to manipulate in applications. This easiness is the reason why extreme points of such models (probability intervals, possibility distributions,. . .) have been well studied. Yet, imprecise cumulative distributions (a.k.a. p-boxes) constitute an important exception, as the characterization of their extreme points remain to be studied. 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.
Fichier principal
Vignette du fichier
Extreme points_Revised.pdf (448.02 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01618340 , version 1 (17-10-2017)

Identifiers

Cite

Ignacio Montes, Sébastien Destercke. On extreme points of p-boxes and belief functions. Annals of Mathematics and Artificial Intelligence, 2017, 81 (3-4), pp.405-428. ⟨10.1007/s10472-017-9562-x⟩. ⟨hal-01618340⟩
101 View
114 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More