Abstract
The paper discusses the different approaches to decision-making using Belief Functions. In particular, I describe Philippe Smets' method of decisionmaking, which transforms a Belief Function into a single probability function, the pignistic probability function. This transformation is sensitive to the choice of frame of discernment, which is often, to a large extent, arbitrary. It thus seems natural to consider all refinements of a frame of discernment and their associated pignistic probability functions and decisions. The main result of the paper is that this is equivalent to the standard approach.
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Dempster, A. P., 67, Upper and Lower Probabilities Induced by a Multi-valued Mapping. Annals of Mathematical Statistics 38: 325–39.
Dempster, A. P., and Kong, A., 87, in discussion of G. Shafer, Probability Judgment in Artificial Intelligence and Expert Systems (with discussion) Statistical Science, 2, No.1, 3–44.
Dubois, D. and Prade, H., 88, Possibility Theory: An Approach to Computerized Processing and Uncertainty, Plenum Press, New York.
Fagin R., and Halpern, J. Y., 89, Uncertainty, Belief and Probability, Proc., International Joint Conference on AI (IJCAI-89), 1161–1167.
Jaffray, J-Y, 92, Bayesian Updating and Belief Functions, IEEE Trans. SMC, 22: 1144–1152.
Shafer, G., 76, A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ.
Shafer, G., 81, Constructive Probability, Synthese, 48: 1–60.
Shafer, G., 90, Perspectives on the Theory and Practice of Belief Functions, International Journal of Approximate Reasoning 4: 323–362.
Smets, Ph. 89, Constructing the Pignistic Probability Function in a Context of Uncertainty, in Proc. 5th Conference on Uncertainty in Artificial Intelligence, Windsor.
Smets, Ph. 90, Decisions and Belief Functions, TIMS-ORSA 90, also research report TR/IRIDIA/90-10, IRIDIA, Université Libre de Bruxelles, 50 av. F. Roosevelt, CP194/6, 1050 Bruxelles, Belgique.
Smets, Ph., and Kennes, R., 89, The Transferable Belief Model: Comparison with Bayesian Models, research report TR/IRIDIA/89-1, IRIDIA, Université Libre de Bruxelles, l50 av. F. Roosevelt, CP194/6, 1050 Bruxelles, Belgique.
Walley, P., 91, Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London.
Wasserman, L. A., 90, Prior Envelopes Based on Belief Functions, Annals of Statistics 18, No.1: 454–464.
Wilson, Nic, 89, Justification, Computational Efficiency and Generalisation of the Dempster-Shafer Theory, Research Report no. 15, June 1989, Dept. of Computing and Mathematical Sciences, Oxford Polytechnic, to appear in Artificial Intelligence.
Wilson, Nic, 91a, A Monte-Carlo Algorithm for Dempster-Shafer Belief, Proc. 7th Conference on Uncertainly in Artificial Intelligence, B. D'Ambrosio, P. Smets and P. Bonissone (eds.), Morgan Kaufmann, 414–417.
Wilson, Nic, 91b, The Representation of Prior Knowledge in a Dempster-Shafer Approach, Proceedings of the DRUMS workshop on Integration of Uncertainty Formalisms, Blanes, Spain, June 1991; also Research Report, Department of Computer Science, Queen Mary and Westfield College, University of London, El 4NS.
Wilson, Nic, 92a, How Much Do You Believe?, International Journal of Approximate Reasoning, 6, No. 3, 345–366.
Wilson, Nic, 92b, Some Theoretical Aspects of the Dempster-Shafer Theory, PhD thesis, Oxford Polytechnic, May 1992.
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© 1993 Springer-Verlag Berlin Heidelberg
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Wilson, N. (1993). Decision-making with Belief Functions and pignistic probabilities. In: Clarke, M., Kruse, R., Moral, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1993. Lecture Notes in Computer Science, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028222
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DOI: https://doi.org/10.1007/BFb0028222
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