A Discrete Choquet Integral for Ordered Systems

Abstract : A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical non-negative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on the set system. It is shown that the general Choquet integral can be computed by a simple Monge-type algorithm for so-called intersection systems, which include as a special case weakly union-closed families. Generalizing Lovász' classical characterization, we give a characterization of the superadditivity of the Choquet integral relative to a capacity on a union-closed system in terms of an appropriate model of supermodularity of such capacities.
Liste complète des métadonnées

Littérature citée [22 références]  Voir  Masquer  Télécharger

https://halshs.archives-ouvertes.fr/halshs-00563926
Contributeur : Michel Grabisch <>
Soumis le : lundi 7 février 2011 - 15:54:25
Dernière modification le : mardi 27 mars 2018 - 11:48:05
Document(s) archivé(s) le : dimanche 8 mai 2011 - 03:41:00

Fichiers

fss10-ulrich.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Ulrich Faigle, Michel Grabisch. A Discrete Choquet Integral for Ordered Systems. Fuzzy Sets and Systems, Elsevier, 2011, 168 (1), pp.3-17. 〈10.1016/j.fss.2010.10.003〉. 〈halshs-00563926〉

Partager

Métriques

Consultations de la notice

275

Téléchargements de fichiers

235