Making Decisions with Belief Functions
This work provides a theoretical extension for researchers in uncertainty reasoning, but it is incremental as it builds on existing frameworks without broad practical impact.
The paper addresses the lack of a formal decision-making procedure in Shafer's theory of belief functions by proposing a probabilistic interpretation of an assumption to disambiguate decisions, proving it yields identical expected values to probabilistic analysis and extending decision analysis methodology for belief functions.
A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning problems, lacks a formal procedure 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 assumption 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 assumption. In addition, we show how the decision analysis methodology frequently employed in probabilistic reasoning can be extended for use with belief functions.