Abstract
Evidential Markov chains (EMCs) are a generalization of classical Markov chains to the Dempster-Shafer theory, replacing the involved states by sets of states. They have been proposed recently in the particular field of an image segmentation application, as hidden models. With the aim to propose them as a more general tool, this paper explores new theoretical aspects about the conditioning of belief functions and the comparison to classical Markov chains and HMMs will be discussed. New computation tools based on matrices are proposed. The potential application domains seem promising in the information-based decision-support systems and an example is given.
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References
Dubois, D., Moral, S., Prade, H.: Belief change rules in ordinal and numerical uncertainty theories. In: Dubois, H.P.D. (ed.) Belief Change, pp. 311–392. Kluwer, Dordrecht (1998)
Dubois, D., Prade, H.: A set theoretical view of belief functions. Int. J. Gen. Systems 12, 193–226 (1986)
Fouque, L., Appriou, A., Pieczynski, W.: An evidential markovian model for data fusion and unsupervised image classification. In: Proc. of 3rd Int. Conf. on Information Fusion, FUSION 2000, Paris, France, pp. YuB4–25–TuB4–31 (2000)
Freedman, D.: Markov chains. Holden-Day (1971)
Grabisch, M., Murofushi, T., Sugeno, M.: Fuzzy Measures and Integrals. Physica-Verlag (2000)
Haenni, R.: Ignoring ignorance is ignorant. Technical report, Center for Junior Research Fellows, University of Konstanz (2003)
Lanchantin, P., Pieczynski, W.: Chaînes et arbres de markov évidentiels avec applications à la segmentation des processus non stationnaires. Revue Traitement du Signal 22 (2005)
McClelland, C.A.: World event/interaction survey codebook (icpsr 5211) inter-university consortium for political and social research, Ann Arbor (1976)
Nuel, G., Prum, B.: Analyse statistique des séquences biologiques. Editions Hermès, Labvoisier, Paris (2007)
Pieczynski, W.: Multisensor triplet markov chain and theory of evidence. Int. J. Approximate Reasoning 45, 1–16 (2007)
Rabiner, L.R.: A tutorial on hidden markov models and selected applications in speech recognition. Proc. of IEEE 77(2), 257–286 (1989)
Schrodt, P.A.: Forecasting conflict in the balkans using hidden markov model (2000)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Shafer, G.: Propagating belief functions in qualitative markov trees. Int. J. Approximate Reasoning 1, 349–400 (1987)
Smets, P.: Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approximate Reasoning 9, 1–35 (1993)
Smets, P.: The application of the matrix calculus to belief functions. Int. J. Approximate Reasoning 31, 1–30 (2002)
Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)
Soubaras, H.: An evidential measure of risk in evidential markov chains. In: Sossai, C., Chemello, G. (eds.) Symbolic and Qualitative Approaches to Reasoning with Uncertainty - 10th ECSQARU, Verona, Italy, pp. 863–874. Springer, Heidelberg (2009)
Soubaras, H., Mattioli, J.: Une approche markovienne pour la prévision du risque. In: Proc. of 7th Congrès int. Pluridisciplinaire Qualité et Sûreté de Fonctionnement, QUALITA 2007, Tanger, Maroc, pp. 64–71 (2007)
Xu, H., Smets, P.: Reasoning in evidential networks with conditional belief functions. Int. J. Approximate Reasoning 14, 155–185 (1996)
Yaghlane, A.B., Denœux, T., Mellouli, K.: Coarsening approximations of belief functions. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, p. 362. Springer, Heidelberg (2001)
Yaghlane, B.B., Mellouli, K.: Inference in directed evidential networks based on the transferable belief model. Int. J. Approximate Reasoning 48, 399–418 (2008)
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Soubaras, H. (2010). On Evidential Markov Chains. 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_13
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DOI: https://doi.org/10.1007/978-3-642-10728-3_13
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