A conjoint measurement approach to the discrete Sugeno integral

Denis Bouyssou (1) , Thierry Marchant (2) , Marc Pirlot (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 Department of Data Analysis
3 Faculté polytechnique de Mons

In a recent paper (European Journal of Operational Research, 158, 271–292, 2004), S. Greco, B. Matarazzo and R. Słowinski 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. Słowi´nski 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.

Mots clés: MCDM; Sugeno integral; conjoint measurement

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Denis Bouyssou, Thierry Marchant, Marc Pirlot. A conjoint measurement approach to the discrete Sugeno integral. 2006. ⟨hal-00119002⟩