Influence diagrams with partially ordered preferences

Imprecision in probability values (represented through credal sets) allows a more realistic modelling of uncertainty in decision problems. Uncertainties often lead to partially ordered preferences and, consequently, different criteria of choice may be taken into account. In this paper, we present an algorithm that evaluates an extended version of influence diagrams, where chance variables represent the uncertainty about states of the nature through a set of probability measures. Criteria for handling partially ordered preferences (Γ-maximin, Γ-maximax, “Γ-maximix”, interval dominance, maximality and E-admissibility) are reviewed. The developed algorithm is based on some graph-theoretic properties of Bayesian and credal networks and require the use of multilinear programming techniques for finding optimal strategies.