Abstract
In a recent paper (European Journal of Operational Research,158, 271-292, 2004), S. Greco, B. Matarazzo and R. Sowi´ nski have stated without proof a result characterizing binary relations on product sets that can be represented using a dis- crete 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 pur- pose 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. Sowi´ 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.
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