G. Anandalingam and C. C. White, A penalty function approach to alternative pairwise comparisons in ISMAUT, IEEE Transactions on Systems, Man, and Cybernetics, vol.23, issue.1, p.330333, 1993.
DOI : 10.1109/21.214795

S. Arnborg, D. Corneil, and A. Proskurowski, Complexity of nding embeddings in a k-tree, SIAM J. Algebraic Discrete Methods, vol.8, p.277284, 1987.

F. Bacchus and A. Grove, Graphical models for preference and utility, Proc. of UAI, pp.3-10, 1995.

A. Berry, J. Bordat, P. Heggernes, G. Simonet, and Y. Villanger, A wide-range algorithm for minimal triangulation from an arbitrary ordering, Journal of Algorithms, vol.58, issue.1, p.3366, 2006.
DOI : 10.1016/j.jalgor.2004.07.001
URL : https://hal.archives-ouvertes.fr/lirmm-00269411

U. Bertele and F. Brioschi, Nonserial dynamic programming, 1972.

J. Blythe, Visual exploration and incremental utility elicitation, Proc. of AAAI, pp.526-532, 2002.

H. Bodlaender, J. Gilbert, T. Hafsteinsson, and H. Kloks, Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree, Journal of Algorithms, vol.18, issue.2, p.238255, 1995.
DOI : 10.1006/jagm.1995.1009
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.7198

C. Boutilier, A POMDP formulation of preference elicitation problems, Proc. of AAAI, pp.239-246, 2002.

C. Boutilier, F. Bacchus, and R. Brafman, UCP-networks ; a directed graphical representation of conditional utilities, Proc. of UAI, pp.56-64, 2001.

C. Boutilier, R. Brafman, C. Domshlak, H. Hoos, and D. Poole, CP-nets : A tool for representing and reasoning with conditional ceteris paribus preference statements, Journal of Articial Intelligence Research, vol.21, p.135191, 2004.

C. Boutilier, R. Brafman, C. Domshlak, H. Hoos, and D. Poole, Preference-Based Constrained Optimization with CP-Nets, Computational Intelligence, vol.14, issue.2, pp.137-157, 2004.
DOI : 10.1109/5254.708432

D. Bouyssou, T. Marchant, P. Perny, M. Pirlot, A. Tsoukiàs et al., Evaluation and decision models : a critical perspective, 2000.
DOI : 10.1007/978-1-4615-1593-7

R. Brafman and C. Domshlak, Introducing variable importance tradeos into CPnets, Proc. of UAI, p.6976, 2002.

D. Braziunas and C. Boutilier, Local utility elicitation in GAI models, Proc. of UAI, p.4249, 2005.

D. Braziunas and C. Boutilier, Minimax regret-based elicitation of generalized additive utilities, Proc. of UAI, 2007.

D. Braziunas and C. Boutilier, Elicitation of factored utilities, p.7992, 2008.

U. Chajewska and D. Koller, Utilities as random variables : Density estimation and structure discovery, Proc. of UAI, p.6371, 2000.

G. Choquet, Theory of capacities, Annales de l'institut Fourrier, pp.131-295, 1953.

E. Dahlhaus and M. Karpinski, An ecient parallel algorithm for the minimal elimination ordering (MEO) of an arbitrary graph, Foundations of Computer Science, Annual IEEE Symposium on, vol.0, p.454459, 1989.

G. Debreu, Continuity properties of paretian utility, International Economic Review, vol.5, p.285293, 1964.

R. Dechter, Constraint processing, 2003.

T. Degris, Apprentissage par Renforcement dans les Processus de Décision Markoviens Factorisés, Thèse de doctorat, LIP6/AnimatLab, 2007.

J. Dubus, C. Gonzales, and P. Perny, Choix multiattribut à l'aide de réseaux GAI de forte densité, p.2539, 2009.

J. Dubus, C. Gonzales, and P. Perny, Choquet optimization using GAI networks for multiagent/multicriteria decision-making, dans Algorithmic Decision Theory, Lectures Notes in Articial Intelligence, p.377389, 2009.

J. Dubus, C. Gonzales, and P. Perny, Fast recommendations using GAI models, dans IJCAI'09, International Joint Conference on Articial Intelligence, p.1896, 1901.
URL : https://hal.archives-ouvertes.fr/hal-01295846

J. Dubus, C. Gonzales, and P. Perny, Multiobjective optimization using GAI models, dans IJCAI'09 International Joint Conference on Articial Intelligence, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01295848

Y. Engel and M. P. Wellman, CUI networks : A graphical representation for conditional utility independence, Proc. of AAAI, p.83112, 2006.

P. C. Fishburn, Utility Theory for Decision Making, 1970.

L. Galand, Méthodes exactes pour l'optimisation multicritère dans les graphes : recherche de solutions de compromis, Thèse de doctorat, pp.6-6, 2008.

M. R. Garey and D. S. Johnson, Computers and Intractability : A Guide to the Theory of NP-Completeness, 1979.

F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, Journal of Combinatorial Theory, Series B, vol.16, issue.1, p.4756, 1974.
DOI : 10.1016/0095-8956(74)90094-X

B. Golden and P. Perny, Innite order lorenz dominance for fair multiagent optimization, Proc. of AAMAS, p.383390, 2010.

M. C. Golumbic, Triangulated graphs, Algorithmic Graph Theory and Perfect Graphs, p.98100, 1980.

C. Gonzales and P. Perny, GAI networks for utility elicitation, Proc. of KR, p.224234, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01501402

C. Gonzales and P. Perny, GAI networks for decision making under certainty, dans R. Brafman et U. Junker, réds, Proceedings of the 19th International Joint Conference on Articial Intelligence workshop on advances in preference handling, p.100105, 2005.

C. Gonzales, P. Perny, and S. Queiroz, Réseaux GAI pour la prise de décision, Revue d, Intelligence Articielle, vol.21, issue.4, p.555587, 2007.

C. Gonzales, P. Perny, and S. Queiroz, Preference aggregation with graphical utility models, dans Proceedings of the 23rd AAAI conference on Articial Intelligence, p.10371042, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01303904

M. Grabisch, The application of fuzzy integrals in multicriteria decision making, European Journal of Operational Research, vol.89, issue.3, p.445456, 1996.
DOI : 10.1016/0377-2217(95)00176-X

M. Grabisch and P. Perny, Agrégation multicritère, 2003.

S. Greco, B. Matarazzo, and R. Slowi«ski, Encyclopedia of Management, chap. Decision rules, 2000.

P. Hansen, Bicriterion path problems, dans G. Fandel et T. Gal, réds., Multiple Criteria Decision Making : Theory and Applications, 1980.
DOI : 10.1007/978-3-642-48782-8_9

E. Jacquet-lagrèze, La modélisation des préférences : préordres, quasi-ordres et relations oues, Thèse de doctorat, 1975.

J. Jaray, On the maximum probability which is consistent with a convex capacity, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.3, p.2734, 1995.

K. Kask and R. Dechter, Branch and bound with mini-bucket heuristics, dans IJCAI'99, International Joint Conference on Articial Intelligence, p.426433, 1999.

R. L. Keeney and H. Raia, Decisions with multiple objectives -preferences and value tradeos, 1993.

M. Kostreva and W. Ogryczak, Linear optimization with multiple equitable criteria, RAIRO - Operations Research, vol.33, issue.3, p.275297, 1999.
DOI : 10.1051/ro:1999112

S. Kullback and R. Leibler, On information and suciency, Annals of Mathematical Statistics, vol.22, p.7986, 1951.

J. Larrosa and T. Schiex, In the quest of the best form of local consistency for weighted csp, Proc. of IJCAI'03, 2003.

M. Laumanns, L. Thiele, K. Deb, and E. Zitzler, Combining Convergence and Diversity in Evolutionary Multiobjective Optimization, Evolutionary Computation, vol.9, issue.3, p.263282, 2002.
DOI : 10.1109/4235.797969

H. Leimer, Optimal decomposition by clique separators, Discrete Mathematics, vol.113, issue.1-3, p.99123, 1993.
DOI : 10.1016/0012-365X(93)90510-Z

R. D. Luce, Semiorders and a Theory of Utility Discrimination, Econometrica, vol.24, issue.2, p.415426, 1956.
DOI : 10.2307/1905751

A. Madsen and K. Olesen, Maximal prime subgraph decomposition of Bayesian Networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol.32, p.2131, 2002.

H. Montgomery, Image theory and dominance search theory: How is decision making actually done?, Acta Psychologica, vol.66, issue.3, p.221224, 1987.
DOI : 10.1016/0001-6918(87)90035-7

T. Murofushi and M. Sugeno, A theory of fuzzy measures: Representations, the Choquet integral, and null sets, Journal of Mathematical Analysis and Applications, vol.159, issue.2, p.532549, 1991.
DOI : 10.1016/0022-247X(91)90213-J

D. Nilsson, An ecient algorithm for nding the M most probable congurations in probabilistic expert systems, Statistics and Computing, vol.8, issue.2, p.159173, 1998.

W. Ogryczak, Inequality measures and equitable approaches to location problems, European Journal of Operational Research, vol.122, issue.2, p.374391, 2000.
DOI : 10.1016/S0377-2217(99)00240-4

T. Ohtsuki, A fast algorithm for nding an optimal ordering in the vertex elimination on a graph, SIAM J. Computing, vol.5, p.133145, 1976.

C. H. Papadimitriou and Y. Yannakakis, On the approximability of trade-os and optimal access of web sources, Proc. of FOCS, 2000.

A. Para and P. Scheer, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics, vol.79, issue.1-3, p.171188, 1997.
DOI : 10.1016/S0166-218X(97)00041-3

J. Pearl, Probabilistic Reasoning in Intelligent Systems, 1988.

P. Perny and O. Spanjaard, Near admissible algorithms for multiobjective search, Proc. of ECAI, p.490494, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01303000

P. Perny, O. Spanjaard, and L. Storme, A decision-theoretic approach to robust optimization in multivalued graphs, Annals of Operations Research, vol.25, issue.6, pp.317-341, 2006.
DOI : 10.1007/s10479-006-0073-0
URL : https://hal.archives-ouvertes.fr/hal-01170404

B. W. Peyton, Minimal orderings revisited, SIAM J. Matrix Analysis and Applications, p.271294, 2001.
DOI : 10.2172/9844
URL : http://digital.library.unt.edu/ark:/67531/metadc791747/m2/1/high_res_d/9844.pdf

S. Queiroz, Modèles graphiques décomposables pour la décision individuelle et collective, Thèse de doctorat, pp.6-6, 2008.

D. Rose, Triangulated graphs and the elimination process, Journal of Mathematical Analysis and Applications, vol.32, issue.3, p.597609, 1970.
DOI : 10.1016/0022-247X(70)90282-9

D. Rose, R. Tarjan, and G. Lueker, Algorithmic Aspects of Vertex Elimination on Graphs, SIAM Journal on Computing, vol.5, issue.2, p.266283, 1976.
DOI : 10.1137/0205021

M. Roubens and P. Vincke, Preference Modelling, 1985.
DOI : 10.1007/978-3-642-46550-5

B. Roy, Méthodologie multicritère d'aide à la décision, 1985.

L. Savage, The Foundations of Statistics, 1954.

D. Schmeidler, Integral representation without additivity, Proceedings of the American Mathematical Society, p.255261, 1986.
DOI : 10.1090/S0002-9939-1986-0835875-8

A. K. Sen and J. E. Foster, On economic inequality, 1997.
DOI : 10.1093/0198281935.001.0001

G. Shafer and P. P. Shenoy, Probability propagation, Annals of Mathematics and Artificial Intelligence, vol.13, issue.1-4, p.327352, 1990.
DOI : 10.1007/BF01531015

L. Shapley, Cores of convex games, International Journal of Game Theory, vol.57, issue.1, p.1122, 1971.
DOI : 10.1007/BF01753431

P. Shenoy and G. Shafer, Axioms for probability and belief-function propagation, Proc. of UAI, p.169198, 1990.

K. Shoikhet and D. Geiger, A practical algorithm for nding optimal triangulations, Proc. of AAAI, p.185190, 1997.

R. Steuer and E. Choo, An interactive weighted Tchebyche procedure for multiple objective programming, Mathematical Programming, p.326344, 1983.

M. Sugeno, Theory of fuzzy integrals and its applications, Thèse de doctorat, 1974.

R. E. Tarjan and M. Yannakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs and selectively reduce hypergraphs, SIAM J. Computing, vol.13, p.566579, 1984.

F. Van-den-eijkhof and H. L. Bodlaender, Safe reduction rules for weighted treewidth, Lecture Notes in Computer Science, vol.2573, p.176185, 2002.

V. V. Vazirani, Approximation Algorithms, 2001.
DOI : 10.1007/978-3-662-04565-7

P. Vincke, Aide Multicritère à la Décision , Editions de l, 1989.

J. Von-neumann and O. Morgenstern, Theory of games and economic behaviour, 1947.

P. P. Wakker, Additive Representations of Preferences, A New Foundation of Decision Analysis, 1989.

M. Weber, Decision making with incomplete information, European Journal of Operational Research, vol.28, issue.1, p.4457, 1987.
DOI : 10.1016/0377-2217(87)90168-8

C. C. White, S. Dozono, and W. T. Scherer, An interactive procedure for aiding multiattribute alternative selection, Omega, vol.11, issue.2, p.212214, 1983.
DOI : 10.1016/0305-0483(83)90011-7

A. Wierzbicki, On the completeness and constructiveness of parametric characterizations to vector optimization problems, Operations-Research-Spektrum, vol.22, issue.2, p.7387, 1986.
DOI : 10.1287/mnsc.22.6.652

R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man and Cybernetics, vol.18, p.183190, 1988.

M. Yannakakis, Computing the minimum ll-in is NP-complete, SIAM Journal on Discrete Mathematics, vol.2, p.7779, 1981.

L. Vice-président-du-conseil-scientique-chargé-de-la-recherche-de-l-'université and P. Les, une représentation graphique compacte et expressive des préférences d'un décideur en Décision Multiattribut, c'est-à-dire dans des situations où les alternatives sur lesquelles portent les choix du décideur sont décrites à l'aide d'un ensemble d'attributs (de caractéristiques) L'exploitation de leur structure graphique permet de dénir des procédures ecaces d'élicitation de préférences (détermination des préférences à l'aide de questionnaires) ainsi que des algorithmes assez performants de prise de décision (calcul de l'alternative préférée du décideur ou des k meilleures alternatives) Le but de cette thèse est double. Tout d'abord elle vise à étendre les algorithmes de prise de décision dans des cas où les réseaux GAI sont denses, c'est-à-dire dans des situations où leur structure ne permet pas aux algorithmes de l'état de l'art de s'exécuter en un temps raisonnable . Pour cela, une nouvelle méthode de triangulation approchée a été développée, qui produit des réseaux GAI approchés sur lesquels des mécanismes d'inférence adaptés permettent d'obtenir les alternatives optimales des réseaux GAI d'origine. Ensuite, elle propose de nouvelles méthodes d'inférence en Décision multicritère

. Mots-clés, Aide à la décision, décision multiattribut, décision multicritère, modélisation des préférences, optimisation combinatoire, graphes