Abstract
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.
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References
J. A. Barnett, Computational Methods for a Mathematical Theory of Evidence: Part II. Forthcoming.
Jacob, Ars Conjectandi, 1713.
A. P. Dempster, “On direct probabilities,” J. Roy. Statist. Soc. Ser. B 25, 1963, 102–107.
A. P. Dempster, “New methods for reasoning toward posterior distributions based on sample data,” Ann. Math. Statis. 37, 1967, 355–374.
A. P. Dempster, “Upper and lower probabilities induced by a multivalued mapping,” Ann. Math. Statis. 38, 1967, 325–339.
A. P. Dempster, “Upper and lower probability inferences based on a sample from a finite univariant population,” Biometrika 54, 1967, 515–528.
A. P. Dempster, “Upper and lower probabilities generated by a random closed interval,” Ann. Math. Statis. 39, (3), 1968, 957–966.
A. P. Dempster, “A generalization of Bayesian inference,” J. Roy. Statis. Soc. Ser. B 30, 1968, 205–247.
A. P. Dempster, “Upper and lower probability inferences for families of hypotheses with monotone density ratios,” Ann. Math. Statis. 40, 1969, 953–969.
R. O. Duda, P. E. Hart, and N. J. Nilsson, Subjective Bayesian methods for rule-based inference systems. Stanford Research Institute, Technical Report 124, January 1976.
L. Friedman, Extended plausible inference. These proceedings.
T. Garvey, J. Lowrance, M. Fischler, An inference technique for integrating knowledge from disparate sources. These proceedings.
F. Hayes-Roth and V. R. Lesser, “Focus of Attention in the Hearsay–II Speech-Understanding System,” in IJCAI77, pp. 27–35, Cambridge, MA, 1977.
H. E. Pople. Jr.,“The formation of composite hypotheses in diagnostic problem solving: an exercise in synthetic reasoning,” in Proc. Fifth International Joint Conference on Artificial Intelligence, pp. 1030–1037, Dept. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa., 1977.
G. Shafer, “A theory of statistical evidence,” in W. L. Harper and C. A. Hooker (eds.), Foundations and Philosophy of Statistical Theories in Physical Sciences, Reidel, 1975.
G. Shafer, A Mathematical Theory Of Evidence, Princeton University Press, Princeton, New Jersey, 1976.
E. H. Shortliffe, Artificial Intelligence Series, Volume 2: Computer-Based Medical Consultations: MYCIN, American Elsevier, Inc., N. Y., chapter IV, 1976.
L. A. Zadeh, “Fuzzy sets,” Information and Control 8, 1965, 338–353.
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Barnett, J.A. (2008). Computational Methods for A Mathematical Theory of Evidence. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_8
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DOI: https://doi.org/10.1007/978-3-540-44792-4_8
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