In the area of decision-making under uncertainty, the use of fuzzy integrals, most notably the Choquet integral and its variants, has attracted much attention in recent years. It is a powerful and elegant way to extend the traditional model of (subjective) expected utility (on this model, see Fishburn, 1970, 1982). Indeed, integrating with respect to a non-necessarily additive measure allows to weaken the independence hypotheses embodied in the additive representation of preferences underlying the expected utility model that have often been shown to be violated in experiments (see the pioneering experimental findings of Allais, 1953; Ellsberg, 1961). Models based on Choquet integrals have been axiomatized in a variety of ways (see Gilboa, 1987; Schmeidler, 1989; or Wakker, 1989, Chap. 6. For related works in the area of decision-making under risk, see Quiggin, 1982; and Yaari, 1987). Recent reviews of this research trend can be found in Chateauneuf and Cohen (2000), Schmidt (2004), Starmer (2000) and Sugden (2004).
More recently, still in the area of decision-making under uncertainty, Dubois, Prade, and Sabbadin (2000b) have suggested to replace the Choquet integral by a Sugeno integral (see Sugeno, 1974, 1977), the latter being a kind of “ordinal counterpart” of the former, and provided an axiomatic analysis of this model (special cases of the Sugeno integral are analyzed in Dubois, Prade, & Sabbadin 2001b. For a related analysis in the area of decision-making under risk, see Hougaard & Keiding, 1996). Dubois, Marichal, Prade, Roubens, and Sabbadin (2001a) offer a lucid survey of these developments.
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Bouyssou, D., Marchant, T., Pirlot, M. (2009). A Conjoint Measurement Approach to the Discrete Sugeno Integral. In: Brams, S.J., Gehrlein, W.V., Roberts, F.S. (eds) The Mathematics of Preference, Choice and Order. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79128-7_6
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