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- An axiomatisation of discrete possibilistic Choquet integrals

Auteur(s): Dubois Didier, Rico A.(Corresp.)

Conference: Foundations of Utility and Risk 2016 (FUR) (Warwick, GB, 2016-06-27)


Necessity (resp. possibility) measures are very simple representations of epistemic uncertainty due to incomplete knowledge. In the present work, a characterization of Choquet integral with respect to a possibility or a necessity measure is proposed, understood as a criterion for decision under uncertainty. This kind of criterion has the merit to be very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decision-maker preferences only reflect the plausibility ordering between states of nature.