  When the information about uncertainty cannot be quantified in a simple,
probabilistic way, the topic of possibilistic decision theory is often a
natural one to consider. The development of possibilistic decision theory has
lead to a series of possibilistic criteria, e.g pessimistic possibilistic
qualitative utility, possibilistic likely dominance, binary possibilistic
utility and possibilistic Choquet integrals. This paper focuses on sequential
decision making in possibilistic decision trees. It proposes a complexity study
of the problem of finding an optimal strategy depending on the monotonicity
property of the optimization criteria which allows the application of dynamic
programming that offers a polytime reduction of the decision problem. It also
shows that possibilistic Choquet integrals do not satisfy this property, and
that in this case the optimization problem is NP - hard.
