13 The Dempster - Shafer Theory of Evidence

The drawbacks of pure probabilistic methods and of the certainty factor model have led us in recent years to consider alternate approaches. Particularly appealing is the mathematical theory of evidence developed by Arthur Dempster. We are convinced it merits careful study and interpretation in the context of expert systems. This theory was first set forth by Dempster in the 1960s and subsequently extended by Glenn Sharer. In 1976, the year after the first description of CF’s appeared, Shafer published A Mathematical Theory of Evidence (Shafer, 1976). Its relevance to the issues addressed in the CF model was not immediately recognized, but recently researchers have begun to investigate applications of the theory to expert systems (Barnett, 1981; Friedman, 1981; Garvey et al., 1981). We believe that the advantage of the Dempster-Shafer theory over previous approaches is its ability to model the narrowing of the hypothesis set with the accumulation of evidence, a process that characterizes diagnostic reasoning in medicine and expert reasoning in general. An expert uses evidence that, instead of bearing on a single hypothesis in the original hypothesis set, often bears on a larger subset of this set. The functions and combining rule of the Dempster-Shafer theory are well suited to represent this type of evidence and its aggregation. For example, in the search for the identity of an infecting organism, a smear showing gram-negative organisms narrows the hypothesis set of all possible organisms to a proper subset. This subset can also be thought of as a new hypothesis: the organism is one of the gram-negative organisms. However, this piece of evidence gives no information concerning the relative likelihoods of the organisms in the subset. Bayesians might assume equal priors and distribute the weight of this evidence equally among the gram-negative organisms, but, as Shafer points out, they would thus fail to distinguish between uncertainty, or lack of" knowledge, and