Games and Decisions 2

Qualitative decision theory: the possibilistic setting

speaker: Didier Dubois (IRIT, Toulouse)

abstract: Decision theory is a very sophisticated formal approach that often relies on probabilities and numerical utility functions. In some decision applications, for instance multicriteria decision-making in on-line recommender systems, numerical approaches are often questionable because it is hard to elicit numerical values quantifying preference, criteria importance or uncertainty. Sometimes multicriteria decision-making methods come down to number-crunching recipes with debatable foundations. One way out of this difficulty is to adopt a qualitative approach where the basic operations are maximum and minimum. It yields methods that enjoy a property of scale invariance, which insures their robustness. One of the most sophisticated aggregation operation making sense on qualitative scales is Sugeno integral. It is qualitative, hence not too demanding for elicitation, and it assumes commensurability between preference intensity and criteria importance or similarly, utility and uncertainty. Sugeno integral generalizes min and max to prioritized versions thereof, where degrees of priority are viewed as satisfaction thresholds assigned to groups of criteria. In this framework probability theory is replaced by possibility theory. The aim of this talk is to provide an introduction to formal foundations of this topic. In particular we shall briefly highlight the following points - Sugeno integral can be viewed as the qualitative counterpart of a lower expectation and of a Choquet integral. - Qualitative decision criteria based on Sugeno integral can be axiomatized in the style of Savage theory - Qualitative criteria suffer from a lack of discrimination power and violate the strict Pareto property. It can be remedied by lexicographic refinements - Qualitative counterparts of cumulative prospect theory exist, for qualitative reasoning with pros and cons.

References to works of the author's team

J.-F. Bonnefon , D. Dubois, H. Fargier, S. Leblois, Qualitative heuristics for balancing the pros and the cons, Theory and Decision, 65:71-95 (2008).

Miguel Couceiro, Didier Dubois, Henri Prade, Tamas Waldhauser. Decision-making with Sugeno integrals: DMU vs. MCDM. European Conference on Artificial Intelligence (ECAI 2012), Montpellier, IOS Press, Frontiers in Artificial Intelligence and Applications 242, p. 288-293, 2012.

D. Dubois, H. Fargier, J.-F. Bonnefon. On the qualitative comparison of decisions having positive and negative features. Journal of Artificial Intelligence Research, AAAI Press, Vol. 32, p. 385-417, 2008.

D. Dubois, H. Fargier, Making Discrete Sugeno Integrals More Discriminant, International Journal of Approximate Reasoning, 50, 2009, 880-898

D. Dubois, H. Fargier, H. Prade, R. Sabbadin. A survey of qualitative decision rules under uncertainty. In : Decision-making Process- Concepts and Methods (D. Bouyssou, D. Dubois, M. Pirlot, H. Prade, Eds.), ISTE London & Wiley, Chap. 11, p. 435-473, 2009.

D. Dubois, H. Fargier. Capacity refinements and their application to qualitative decision evaluation Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009, Verona ,Italy), C. Sossai , G. Chemello (Eds.), Springer, LNAI 5590, p. 311-322, 2009.

D. Dubois, H. Prade. R. Sabbadin. Decision theoretic foundations of qualitative possibility theory. European Journal of Operational Research, 128, 459-478, 2001.

D. Dubois, H. Fargier, H. Prade, P. Perny . Qualitative Decision Theory: From Savage's Axioms to Nonmonotonic Reasoning . Journal of the ACM, V. 49 N. 4, p. 455-495, juillet 2002.

D. Dubois, H. Fargier, P. Perny . Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach. Artificial Intelligence, V. 148, p. 219-260, 2003 (Corrigendum, V. 171, p. 361-362, 2007.)

H. Fargier and R. Sabbadin. Qualitative decision under uncertainty: Back to expected utility. Artificial Intelligence, 164:245-280, 2005.

H. Prade, A. Rico, M. Serrurier, E. Raufaste. Eliciting Sugeno integrals: methodology and a case study In : Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009, Verona ,Italy), C. Sossai , G. Chemello (Eds.), Springer, LNAI 5590, p. 712-723, 2009.

H. Prade, A. Rico, M. Serrurier. Elicitation of Sugeno integrals: A version space learning perpective. In International Symposium on Methodologies for Intelligent Systems (ISMIS 2009), Prague (J. Rauch, Z. Ras, P. Berka, T. Elomaa, Eds.), Springer, LNAI 5722, p. 392-401, 2009.

timetable:
Mon 7 Jul, 10:00 - 11:00, Sala Azzurra
<< Go back