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A conjoint measurement approach to the discrete Sugeno integral

Pirlot, Marc; Marchant, Thierry; Bouyssou, Denis (2009), A conjoint measurement approach to the discrete Sugeno integral, in Brams, S.; Gehrlein, W. V.; Roberts, F. S., The Mathematics of Preference, Choice and Order. Essays in Honor of Peter C. Fishburn, Springer, p. 85-109. 10.1007/978-3-540-79128-7_6

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Type
Chapitre d'ouvrage
Date
2009
Book title
The Mathematics of Preference, Choice and Order. Essays in Honor of Peter C. Fishburn
Book author
Brams, S.; Gehrlein, W. V.; Roberts, F. S.
Publisher
Springer
ISBN
978-3-540-79127-0
Number of pages
420
Pages
85-109
Publication identifier
Metadata
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Author(s)
Pirlot, Marc
Faculté Polytechnique de Mons
Marchant, Thierry
Department of Data Analysis
Bouyssou, Denis cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
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.
Subjects / Keywords
Conjoint measurement; Sugeno integral; MCDM