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

摘要

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 R-* 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. (C) 2019 Elsevier Inc. All rights reserved.