Decision Analysis Using Belief Functions

Abstract

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. Shafer’s theory of belief functions, which explicitly represents the under-constrained 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. We maintain a strict separation between evidence that carries information about a situation and assumptions that may be made for disambiguation of choices. In addition, we show how the decision analysis methodology frequently employed in probabilistic reasoning can be extended for use with belief functions. This generalization of decision analysis allows the use of belief functions within the familiar framework of decision trees.