Titre :

Complementary Lipschitz continuity results for the distribution of intersections or unions of independent random sets in finite discrete spaces

Auteur(s) :

Klein, John [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Titre de la revue :

International Journal of Approximate Reasoning

Éditeur :

Elsevier

Date de publication :

2019-04

ISSN :

0888-613X

Mot(s)-clé(s) en anglais :

random sets
Lipschitz continuity
belief functions
distance
combination rules
information fusion
conflict
α-junctions 1

Discipline(s) HAL :

Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]

Résumé en anglais : [en]

We prove that intersections and unions of independent random sets in finite spaces achieve a form of Lipschitz continuity. More precisely, given the distribution of a random set Ξ, the function mapping any random set ...
Lire la suite >We prove that intersections and unions of independent random sets in finite spaces achieve a form of Lipschitz continuity. More precisely, given the distribution of a random set Ξ, the function mapping any random set distribution to the distribution of its intersection (under independence assumption) with Ξ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the L k norm distance between inclusion func-tionals also known as commonalities. Moreover, the function mapping any random set distribution to the distribution of its union (under independence assumption) with Ξ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the L k norm distance between hitting func-tionals also known as plausibilities. Using the epistemic random set interpretation of belief functions, we also discuss the ability of these distances to yield conflict measures. All the proofs in this paper are derived in the framework of Dempster-Shafer belief functions. Let alone the discussion on conflict measures, it is straightforward to transcribe the proofs into the general (non necessarily epistemic) random set terminology.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL