Prise de décision multiattribut avec le modèle GAI

GAI networks are a graphical model, both compact and expressive, for representingthe preferences of a Decision Maker in the context of Multiattribute Decision Making,i.e., in situations where the set of alternatives among which the Decision Maker has tomake decisions are described as a set of attributes (or features). GAI network's graphi-cal structures are exploited to develop e cient elicitation procedures (determination ofthe Decision Maker's preferences using questionnaires) as well as e ective Decision Ma-king algorithms (e.g., computing the preferred alternative or the k-best alternatives).The goal of this PhD thesis is twofold. First, it extends the aforementioned state-of-the-art Decision Making algorithms to be able to cope with dense GAI networks, i.e., withsituations where the GAI network's treewidth is too high for these algorithms to com-plete in a reasonable amount of time. For this purpose, a new triangulation method hasbeen developed which produces approximated GAI networks on which tailored inferencemechanisms determine the alternatives that are actually optimal for the original GAInetwork. Second, we have proposed new inference algorithms for Multicriteria DecisionMaking. More precisely, new approaches for determining Pareto-optimal sets (exact andapproximate with performance guarantee) and Lorenz-optimal sets have been developed.In addition, we have also proposed new algorithms for computing the optimal solutionsin situations where criteria are aggregated using various operators like OWA (OrderedWeighted Average), Choquet integrals and Tchebyche 's norm.