Summary
In this paper we introduce the relative belief of singletons as a novel Bayesian approximation of a belief function. We discuss its nature in terms of degrees of belief under several different angles, and its applicability to different classes of belief functions.
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References
Aigner, M.: Combinatorial theory. Classics in Mathematics. Springer, New York (1979)
Bauer, M.: Approximation algorithms and decision making in the Dempster-Shafer theory of evidence–an empirical study. International Journal of Approximate Reasoning 17, 217–237 (1997)
Cobb, B.R., Shenoy, P.P.: A comparison of Bayesian and belief function reasoning. Information Systems Frontiers 5(4), 345–358 (2003)
Cuzzolin, F.: Dual properties of relative belief of singletons, IEEE Trans. Fuzzy Systems (submitted, 2007)
Cuzzolin, F.: Relative plausibility, affine combination, and Dempster’s rule, Tech. report, INRIA Rhone-Alpes (2007)
Cuzzolin, F.: A geometric approach to the theory of evidence. IEEE Transactions on Systems, Man and Cybernetics part C (to appear, 2007)
Cuzzolin, F.: Two new Bayesian approximations of belief functions based on convex geometry. IEEE Transactions on Systems, Man, and Cybernetics - Part B 37(4) (August 2007)
Cuzzolin, F.: Geometry of upper probabilities. In: Proceedings of the 3rd Internation Symposium on Imprecise Probabilities and Their Applications (ISIPTA 2003) (July 2003)
Daniel, M.: On transformations of belief functions to probabilities. International Journal of Intelligent Systems, special issue on Uncertainty Processing 21(3), 261–282 (2006)
Dempster, A.P.: Upper and lower probabilities generated by a random closed interval. Annals of Mathematical Statistics 39, 957–966 (1968)
Denoeux, T.: Inner and outer approximation of belief structures using a hierarchical clustering approach. Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9(4), 437–460 (2001)
Denoeux, T., Ben Yaghlane, A.: Approximating the combination of belief functions using the Fast Moebius Transform in a coarsened frame. International Journal of Approximate Reasoning 31(1–2), 77–101 (2002)
Haenni, R., Lehmann, N.: Resource bounded and anytime approximation of belief function computations. International Journal of Approximate Reasoning 31(1–2), 103–154 (2002)
Kramosil, I.: Approximations of believeability functions under incomplete identification of sets of compatible states. Kybernetika 31, 425–450 (1995)
Lowrance, J.D., Garvey, T.D., Strat, T.M.: A framework for evidential-reasoning systems. In: Proceedings of the National Conference on Artificial Intelligence (American Association for Artificial Intelligence, ed.), pp. 896–903 (1986)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Smets, P.: Belief functions versus probability functions. In: Saitta, L., Bouchon, B., Yager, R. (eds.) Uncertainty and Intelligent Systems, pp. 17–24. Springer, Berlin (1988)
Smets, P.: Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate reasoning 9, 1–35 (1993)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. International Journal of Approximate Reasoning 38(2), 133–147 (2005)
Smets, P.: The canonical decomposition of a weighted belief. In: Proceedings of the International Joint Conference on AI, IJCAI 1995, Montréal, Canada, pp. 1896–1901 (1995)
Tessem, B.: Approximations for efficient computation in the theory of evidence. Artificial Intelligence 61(2), 315–329 (1993)
Voorbraak, F.: A computationally efficient approximation of Dempster-Shafer theory. International Journal on Man-Machine Studies 30, 525–536 (1989)
Ben Yaghlane, A., Denoeux, T., Mellouli, K.: Coarsening approximations of belief functions. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 362–373. Springer, Heidelberg (2001)
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Cuzzolin, F. (2008). Semantics of the Relative Belief of Singletons. In: Huynh, VN., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds) Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77664-2_16
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DOI: https://doi.org/10.1007/978-3-540-77664-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77663-5
Online ISBN: 978-3-540-77664-2
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