Influence Diagram Model with Interval-Valued Utilities

Influence diagrams (IDs) are a popular framework representing a decision maker´s belief and preferences about a sequence of decisions to be made under uncertainty. The quantification of IDs which consists of defining conditional probabilities for chance nodes and utility functions for value nodes is not always obvious. In fact, decision makers cannot always provide exact utilities and in some cases, it is more convincible to describe utilities with interval values than precise ones. This paper is about extending general IDs (with precise single-valued parameters) into IDs with interval-valued utilities. Such extension is interesting because it enables one to model decision making processes in the situation that utilities are represented by interval values. This paper extend Gibbs sampling algorithm to the Bayesian network (BN) containing interval-valued probabilities for approximate inference and propose a method to evaluate IDs with interval-valued utilities based on the BN inference.