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Stochastic dominance with respect to a capacity and risk measures
Grigorova, Miryana - HAL - 2011
also called a capacity, the present paper gives a generalization to the case of a capacity of the classical notion of … quantile function with respect to the given capacity. Characterizations, involving Choquet integrals with respect to a … distorted capacity, are established for the classes of monetary risk measures (defined on the space of bounded real …
Persistent link: https://www.econbiz.de/10009368022
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Capacities and Games on Lattices: A Survey of Result
Grabisch, Michel - HAL - 2006
We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations...
Persistent link: https://www.econbiz.de/10010750699
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A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid
Grabisch, Michel; Labreuche, Christophe - HAL - 2008
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a...
Persistent link: https://www.econbiz.de/10010750818
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A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid
Grabisch, Michel; Labreuche, Christophe - HAL - 2010
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a...
Persistent link: https://www.econbiz.de/10010603640
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Decision making over imprecise lotteries
Rébillé, Yann - HAL - 2005
Since von Neuman and Morgenstern's (1944) contribution to game theory, the expected utility criterion has become the standard functional to evaluate risky prospects. Risky prospects are understood to be lotteries on a set of prizes. In which case a decision maker will receive a precise prize...
Persistent link: https://www.econbiz.de/10010750553
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Second Order Beliefs Models of Choice under Imprecise Risk
Giraud, Raphaël - HAL - 2013
This paper discusses models of choice under imprecise objective proba- bilistic information featuring beliefs about beliefs - second order beliefs. A new model, called Second Order Dual Expected Utility (SODEU) featuring non-additive second order beliefs is introduced, axiomatized and systemati-...
Persistent link: https://www.econbiz.de/10009021746
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Stochastic orderings with respect to a capacity and an application to a financial optimization problem
Grigorova, Miryana - HAL - 2011
called a capacity. We give different characterizations of this relation establishing a link to the notions of distribution … function and quantile function with respect to the given capacity. The Choquet integral is extensively used as a tool. We state … from below concave (resp. convex) capacity. We apply our results to a financial optimization problem whose constraints are …
Persistent link: https://www.econbiz.de/10009246902
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Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches
Grabisch, Michel; Greco, Salvatore; Pirlot, Marc - HAL - 2008
Multi-criteria decision analysis studies decision problems in which the alternatives are evaluated on several dimensions or viewpoints. In the problems we consider in this paper, the scales used for assessing the alternatives with respect to a viewpoint are bipolar and univariate or unipolar and...
Persistent link: https://www.econbiz.de/10010738479
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Cardinal extensions of EU model based on the Choquet integral
Chateauneuf, Alain; Cohen, Michèle - HAL - 2008
This chapter of a collective book aims at presenting cardinal extensions of the EU model, based on the Choquet integral, which allow to take into account observed behaviors as in Allais' paradox under risk or Ellsberg's paradox under uncertainty, where the expected utility model is violated....
Persistent link: https://www.econbiz.de/10010738555
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An empirical study of statistical properties of Choquet and Sugeno integrals
Grabisch, Michel; Raufaste, Eric - HAL - 2008
This paper investigates the statistical properties of the Choquet and Sugeno integrals, used as multiattribute models. The investigation is done on an empirical basis, and focuses on two topics: the distribution of the output of these integrals when the input is corrupted with noise, and the...
Persistent link: https://www.econbiz.de/10010738659