Abstract
Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster’s rule, relative plausibility and belief transforms form one such “epistemic” family, and possess natural rationales within Shafer’s formulation of the theory of evidence. However, the relative belief transform only exists when some mass is assigned to singletons. We show here that relative belief is only a member of a class of “relative mass” mappings, which can be interpreted as lowcost proxies for both plausibility and pignistic transforms.
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References
Burger, T.: Defining new approximations of belief functions by means of Dempster’s combination. In: Proc. of BELIEF 2010 (2010)
Cobb, B.R., Shenoy, P.P.: A Comparison of Methods for Transforming Belief Function Models to Probability Models. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 255–266. Springer, Heidelberg (2003)
Cobb, B., Shenoy, P.: A comparison of Bayesian and belief function reasoning. Information Systems Frontiers 5(4), 345–358 (2003)
Cuzzolin, F.: Two new Bayesian approximations of belief functions based on convex geometry. IEEE Transactions on Systems, Man, and Cybernetics - Part B 37(4), 993–1008 (2007)
Cuzzolin, F.: A geometric approach to the theory of evidence. IEEE Transactions on Systems, Man, and Cybernetics - Part C 38(4), 522–534 (2008)
Cuzzolin, F.: Dual properties of the relative belief of singletons. In: Proc. of the Pacific Rim International Conference on AI, pp. 78–90 (2008)
Cuzzolin, F.: Geometry of relative plausibility and relative belief of singletons. Annals of Mathematics and Artificial Intelligence, 1–33 (2010)
Cuzzolin, F.: Semantics of the relative belief of singletons. In: Workshop on Uncertainty and Logic, Kanazawa, Japan (2008)
Daniel, M.: On transformations of belief functions to probabilities. Int. J. of Intelligent Systems 21(3), 261–282 (2006)
Dempster, A.P.: A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B 30, 205–247 (1968)
Dezert, J., Smarandache, F.: A new probabilistic transformation of belief mass assignment. In: Proc. of the 11th International Conference of Information Fusion, pp. 1–8 (2008)
Haenni, R.: Aggregating referee scores: an algebraic approach. In: 2nd International Workshop on Computational Social Choice, COMSOC 2008, pp. 277–288 (2008)
Lowrance, J., Garvey, T., Strat, T.: A framework for evidential-reasoning systems. In: Proc. of the National Conference on Artificial Intelligence, pp. 896–903 (1986)
Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)
Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66(2), 191–234 (1994)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. IJAR 38(2), 133–147 (2005)
Sudano, J.: Equivalence between belief theories and nave Bayesian fusion for systems with independent evidential data. In: Proc. of the 6th International Conference of Information Fusion, vol. 2, pp. 1239–1243 (2003)
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)
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Cuzzolin, F. (2012). Generalizations of the Relative Belief Transform. In: Denoeux, T., Masson, MH. (eds) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29461-7_13
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DOI: https://doi.org/10.1007/978-3-642-29461-7_13
Publisher Name: Springer, Berlin, Heidelberg
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