On the Combinality of Evidence in the Dempster-Shafer Theory

In the current versions of the Dempster-Shafer theory, the only essential restriction on the validity of the rule of combination is that the sources of evidence must be statistically independent. Under this assumption, it is permissible to apply the Dempster-Shafer . rule to two or more distinct probability distributions. An essential step in the Dempster-Shafer rule of combination of evidence is that of normalization. The validity of normalization is open to question, particularly in application to probability distributions (Zadeh, 1976). At this juncture, the validity of normalization is a controversial issue. In this paper, we construct a relational model for the Dempster-Shafer theory which greatly simplifies the derivation of its main results and cast considerable light on the valldity of the rule of combination. The relational model is augmented with what is called the ball-box analogy, yielding an intuitively simple way of visualizing the concepts of belief and plausibility. t Computer Science Division, University of California, Berkeley, CA 94720. * Department of Computer Science, University of Cincinnati, Cincinnati. OH 45221. Research supported in part by NSF Grant DCR-8513139, NASA Grant NCC-2-275 and NESC Contract N00039·84-C-0243.