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2007-01-09 - Colloque/Article dans les actes avec comité de lecture - Anglais - page(s)

Pirlot Marc , "A conjoint measurement approach to the discrete Sugeno integral: a note on a result of Greco, Matarazzo and Slowinski" in Annales du LAMSADE 2006, Paris Proceedings of the DIMACS-LAMSADE Workshop on Voting Theory and Preference Modelling, Paris, France, 2006

  • Codes CREF : Modèles mathématiques d'aide à la décision (DI1151), Mathématiques (DI1100), Recherche opérationnelle (DI1150)
  • Unités de recherche UMONS : Mathématique et Recherche opérationnelle (F151)
Texte intégral :

Abstract(s) :

(Anglais) In a recent paper (European Journal of Operational Research, 158, 271–292, 2004), S. Greco, B. Matarazzo and R. Slowinski have stated without proof a result characterizing binary relations on product sets that can be represented using a discrete Sugeno integral. To our knowledge, this is the first result about a fuzzy integral that applies to non-necessarily homogeneous product sets and only uses a binary relation on this set as a primitive. This is of direct interest to MCDM. The main purpose of this note is to propose a proof of this important result. Thereby, we study the connections between the discrete Sugeno integral and a non-numerical model called the noncompensatory model. We also show that the main condition used in the result of S. Greco, B. Matarazzo and R. Slowinski can be factorized in such a way that the discrete Sugeno integral model can be viewed as a particular case of a general decomposable representation.