Abstract
Different operations can be used in the theory of belief functions to correct the information provided by a source, given metaknowledge about that source. Examples of such operations are discounting, de-discounting, extended discounting and contextual discounting. In this article, the links between these operations are explored. New interpretations of these schemes, as well as two families of belief function correction mechanisms are introduced and justified. The first family generalizes previous non-contextual discounting operations, whereas the second generalizes the contextual discounting.
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References
Dempster, A.: Upper and Lower Probabilities Induced by Multivalued Mapping. Annals of Mathematical Statistics AMS-38, 325–339 (1967)
Denœux, T., Smets, P.: Classification using Belief Functions: the Relationship between the Case-Based and Model-Based Approaches. IEEE Transactions on Systems, Man and Cybernetics, Part B 36(6), 1395–1406 (2006)
Denœux, T.: Conjunctive and Disjunctive Combination of Belief Functions Induced by Non Distinct Bodies of Evidence. Artificial Intelligence 172, 234–264 (2008)
Dubois, D., Prade, H.: A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. International Journal of General Systems 12, 193–226 (1986)
Elouedi, Z., Mellouli, K., Smets, P.: Assessing sensor reliability for multisensor data fusion with the transferable belief model. IEEE Transactions on Systems, Man and Cybernetics B 34, 782–787 (2004)
Goodman, I.R., Mahler, R.P., Nguyen, H.T.: Mathematics of Data Fusion. Kluwer Academic Publishers, Norwell (1997)
Kohlas, J., Monney, P.-A.: A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems, vol. 425. Springer, Berlin (1995)
Mercier, D.: Fusion d’informations pour la reconnaissance automatique d’adresses postales dans le cadre de la théorie des fonctions de croyance, PhD Thesis, Université de Technologie de Compiègne (December 2006)
Mercier, D., Denœux, T., Masson, M.-H.: A parameterized family of belief functions correction mechanisms. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proceedings of IPMU 2008, Torremolinos, Malaga, June 22-27, pp. 306–313 (2008)
Mercier, D., Quost, B., Denœux, T.: Refined modeling of sensor reliability in the belief function framework using contextual discounting. Information Fusion 9, 246–258 (2008)
Mercier, D., Cron, G., Denœux, T., Masson, M.-H.: Decision fusion for postal address recognition using belief functions. Expert Systems with Applications, part 1 36(3), 5643–5653 (2009)
Pichon, F.: Belief functions: canonical decompositions and combination rules, PhD Thesis, Université de Technologie de Compiègne (March 2009)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Smets, Ph.: Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning 9, 1–35 (1993)
Smets, Ph.: What is Dempster-Shafer’s model? In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer theory of evidence, pp. 5–34. Wiley, New-York (1994)
Smets, Ph.: The canonical decomposition of a weighted belief. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 1995), pp. 1896–1901. Morgan Kaufman, San Mateo (1995)
Smets, Ph.: The Transferable Belief Model for quantified belief representation. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible reasoning and uncertainty management systems, vol. 1, pp. 267–301. Kluwer Academic Publishers, Dordrecht (1998)
Smets, Ph.: Managing Deceitful Reports with the Transferable Belief Model. In: Proceedings of the 8th International Conference On Information Fusion, FUSION 2005, Philadelphia, USA, July 25-29, paper C8-3 (2005)
Smets, Ph., Kennes, R.: The Transferable Belief Model. Artificial Intelligence 66, 191–243 (1994)
Zhu, H., Basir, O.: Extended discounting scheme for evidential reasoning as applied to MS lesion detection. In: Svensson, P., Schubert, J. (eds.) Proceedings of the 7th International Conference on Information Fusion, FUSION 2004, June 2004, pp. 280–287 (2004)
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Mercier, D., Denœux, T., Masson, MH. (2010). Belief Function Correction Mechanisms. In: Bouchon-Meunier, B., Magdalena, L., Ojeda-Aciego, M., Verdegay, JL., Yager, R.R. (eds) Foundations of Reasoning under Uncertainty. Studies in Fuzziness and Soft Computing, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10728-3_11
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DOI: https://doi.org/10.1007/978-3-642-10728-3_11
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