Séminaire Donnees et APprentissage Artificiel
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Models for pessimistic or optimistic decisions under different uncertain scenarios
Intervenant(s) : Giulianella Coletti (University of Perugia, Italy)We consider a problem in the ambit of decisions under uncertainty, i.e., we study situations where a (not necessarily complete) preference relation is given on an arbitrary set of gambles and the decision model of reference is the Choquet expected value with respect to a belief or a plausibility function. For this aim we introduce two rationality principles which are necessary and sufficient conditions for the existence of a belief function or a plausibility function such that the corresponding Choquet integral represents the relation. Nevertheless sometimes a decision maker could be either not able or not interested in giving preferences among gambles, but he could only be able to specify his preferences under the hypothesis that a particular event happens. In other words, he could not be able to express his preference relation under a generic scenario, but could assess it under various scenarios, which are taken into account at the same time. So we need to consider the Choquet expected values with respect to a conditional belief or plausibility function as decision model. As is well known there are several notions of conditioning for belief or plausibility functions in the literature. The choice of the different conditioning notions heavily impacts on the properties of relations represented by the above model.
Giulianella Coletti is a Full Professor of Probability and Mathematical Statistics at the University of Perugia, Italy. She has been Coordinator of the "Dottorato di Ricerca" (Ph.D. school) "Mathematics and Informatics to Handle and Represent Information and knowledge " at University of Perugia since 2003 and Supervisor for the "Dottorato di Ricerca" (Ph.D. school) in Mathematics, Computer Science and Statistics, promoted by University of Florence, University of Perugia and INdAM since 2012. She has also been a member of the Scientific Committee of INdAM (Istituto Nazionale di Alta Matematica) since 2013. Her main fields of interest are: probability, non additive uncertainty measures, decision making, theory of measurements. She is the author of more than 160 articles, 1 book (edited by Kluwer) and she is the editor of 4 books (edited by Elsevier, Springer, Plenum Press, CNR Applied Mathematics Monographs- Giardini Editori ) and of some special issues for international journals.
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