Sequential decision making under ordinal uncertainty: A qualitative alternative to the Hurwicz criterion

This paper focuses on sequential qualitative decision problems, where no probability distribution on the states that may follow an action is available. New qualitative criteria that are based on ordinal uninorms and namely R⁎ and R⁎ are proposed. Like the Hurwicz criterion, the R⁎ and R⁎ uninorms arbitrate between pure pessimism and pure optimism, and generalize the Maximin and Maximax criteria. But contrarily to the Hurwicz criterion they are associative, purely ordinal and compatible with Dynamic Consistency and Consequentialism. These important properties allow the construction of an optimal strategy in polytime, following an algorithm of Dynamic Programming. Making a step further, we then generalize ⁎ to qualitative decision under possibilistic uncertainty, proposing an alternative to the classical optimistic and pessimistic criteria used for the computation of optimal strategies in possibilistic decision trees.

[1]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[2]  Jérôme Lang,et al.  Towards qualitative approaches to multi-stage decision making , 1998, Int. J. Approx. Reason..

[3]  Didier Dubois,et al.  Deciding under Ignorance: In Search of Meaningful Extensions of the Hurwicz Criterion to Decision Trees , 2014, SMPS.

[4]  Régis Sabbadin,et al.  A Possibilistic Model for Qualitative Sequential Decision Problems under Uncertainty in Partially Observable Environments , 1999, UAI.

[5]  Didier Dubois,et al.  Qualitative Decision Theory with Sugeno Integrals , 1998, UAI.

[6]  Matthias C. M. Troffaes,et al.  An Efficient Normal Form Solution to Decision Trees with Lower Previsions , 2008, SMPS.

[7]  Didier Dubois,et al.  Possibility Theory as a Basis for Qualitative Decision Theory , 1995, IJCAI.

[8]  Jean-Yves Jaffray Rational Decision Making With Imprecise Probabilities , 1999, ISIPTA.

[9]  E. McClennen Rationality and Dynamic Choice: Foundational Explorations , 1996 .

[10]  Didier Dubois,et al.  The Use of the Discrete Sugeno Integral in Decision-Making: A Survey , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[11]  Howard Raiffa,et al.  Decision analysis: introductory lectures on choices under uncertainty. 1968. , 1969, M.D.Computing.

[12]  Régis Sabbadin,et al.  Possibilistic Markov decision processes , 2001 .

[13]  Fabio Gagliardi Cozman,et al.  Sequential decision making with partially ordered preferences , 2011, Artif. Intell..

[14]  Ronald R. Yager,et al.  Uninorm aggregation operators , 1996, Fuzzy Sets Syst..