Decision Making with Second‐Order Imprecise Probabilities

Abstract

In decision analysis, uncertainty is usually described in the framework of probability. However, a large number of experimental and theoretical studies showed that a single nature of probability does not accurately capture human preferences. To avoid this drawback, they use imprecise probabilities. But, as decision maker is usually uncertain about first‐order imprecise probabilities, imprecise hierarchical probability models are used. For most of such models, the second levels are precise. There also exist studies on two‐level imprecise hierarchical models, which use imprecise probabilities or possibilities at the second level. Most of these works are based on lower prevision theory leading to a large number of optimization problems. In the present paper, we propose an imprecise hierarchical decision‐making model where the first and the second level are described by interval probabilities. The method associates with the construction of a nonadditive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function.