Valuation-based systems for decision analysis using belief functions

Valuation-based systems (VBS) provide a general framework for representing knowledge and drawing inferences under uncertainty. Recent studies have shown that the VBS can also represent and solve Bayesian decision problems. This paper proposes a decision calculus for belief function theory in the VBS. The proposed calculus uses a parameter whose role is the probabilistic interpretation of an assumption that disambiguates decision problems represented with belief functions. We show that the decision problems can be solved by using local computations with the presented calculus if they are represented in the VBS properly. We also show that the presented calculus can be reduced to the one for Bayesian decision problems when probabilities, instead of belief functions, are given.