GAI networks are a graphical model, both compact and expressive, for representing the 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 to make decisions are described as a set of attributes (or features). GAI network's graphical structures are exploited to develop e cient elicitation pro cedures (determination of the Decision Maker's preferences using questionnaires) as well as e ffective Decision Making 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., with situations where the GAI network's treewidth is to o high for these algorithms to complete in a reasonable amount of time. For this purpose, a new triangulation method has been developed which produces approximated GAI networks on which tailored inference mechanisms determine the alternatives that are actually optimal for the original GAI network. Second, we have prop osed new inference algorithms for Multicriteria Decision Making. More precisely, new approaches for determining Pareto-optimal sets (exact and approximate with performance guarantee) and Lorenz-optimal sets have b een developed. In addition, we have also proposed new algorithms for computing the optimal solutions in situations where criteria are aggregated using various op erators like OWA (Ordered Weighted Average), Choquet integrals and Tchebyche ff's norm.
