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A conjoint measurement view on fuzzy integrals

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					A conjoint measurement view on fuzzy integrals

Denis Bouyssou, Thierry Marchant, Marc Pirlot,

In the field of MCDM, the dominant model is the additive value function model that has
received a thorough axiomatic treatment in the framework of conjoint measurement following
the works of Gérard Debreu and Duncan Luce. This model however implies that criteria are
mutually independent. Choquet and Sugeno integrals have recently attracted much interest in
MCDM as convenient tools to model interactions between criteria.
The purpose of this paper is to review the existing literature on these two models from the
point of view of conjoint measurement, i.e., within a framework in which the only primitive is
a preference relation defined on a product set that does not have to be homogeneous.
Whereas the measurement-theoretic foundations of Choquet and Sugeno integrals have been
well studied in the area of decision making under uncertainty, a comparable analysis is still
lacking in the area of MCDM. Indeed, the very conception of these two techniques implies a
“commensurability” hypothesis that is not easy to formalize within the framework of conjoint
measurement.
We shall first review the various attempts that have been made to axiomatize Choquet and
Sugeno integrals within a classical conjoint measurement framework. We then concentrate on
the Sugeno integral, showing that existing axiomatic analyses of this tool allow suggesting
new and simple interpretation the aggregation it promotes. This will lead to a novel
interpretation of the Sugeno integral that will emphasize its ordinal character and links it with
“noncompensatory” aggregation models. This analysis is builds on uses recent work in the
area by Salvatore Greco, Benedetto Matarazzo and Roman Slowinski.

				
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