Computational Methods for A Mathematical Theory of Evidence

Many knowledge-based expert systems employ numerical schemes to represent evidence, rate competing hypotheses, and guide search through the domain’s problem space. This paper has two objectives: first, to introduce one such scheme, developed by Arthur Dempster and Glen Shafer, to a wider audience; second, to present results that can reduce the computation-time complexity from exponential to linear, allowing this scheme to be implemented in many more systems. In order to enjoy this reduction, some assumptions about the structure of the type of evidence represented and combined must be made. The assumption made here is that each piece of the evidence either confirms or denies a single proposition rather than a disjunction. For any domain in which the assumption is justified, the savings are available. ∗This research is supported by the Defense Advanced Research Projects Agency under Contract No. DAHC15 72 C 0308. Views and conclusions contained in this report are the author’s and should not be interpreted as representing the official opinion or policy of DARPA, the US Government, or any person or agency connected with them. †Originally appeared in Proceedings of the Seventh International Conference on Artificial Intelligence, 1981, 868–875. Also available in Selected Papers on Sensor and Data Fusion, F. A. Sadjadi Editor, SPIE Milestone Series Vol. MS 124, 317–324, 1996. Also published in Classic Works of the Dempster-Shafer Theory of Belief Functions, R. Yager and L. Liu Editors, Springer, 197–216, 2008. ‡Email addresses: [email protected]