Making Decisions with Belief Functions

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evi­ dence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained na­ ture of many reasoning problems, lacks a formal pro­ cedure for making decisions. Clearly, when sufficient information is not available, no theory can prescribe actions without making additional assumptions. Faced with this situation, some assumption must be made if a clearly superior choice is to emerge. In this paper we offer a probabilistic interpretation of a simple assump­ tion that disambiguates decision problems represented with belief functions. We prove that it yields expected values identical to those obtained by a probabilistic analysis that makes the same ass umption. In addi­ tion, we show how the decision analysis methodology frequently employed in probabilistic reasoning can be extended for use with belief functions.