Abstract
In this paper, we study foundations of interval-based possibilistic networks where possibility degrees associated with nodes are no longer singletons but sub-intervals of [0,1]. This extension allows to compactly encode and reason with epistemic uncertainty and imprecise beliefs as well as with multiple expert knowledge. We propose a natural semantics based on compatible possibilistic networks. The last part of the paper shows that computing the uncertainty bounds of any event can be computed in interval-based networks without extra computational cost with respect to standard possibilistic networks.
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References
Ben Amor, N., Benferhat, S., Mellouli, K.: A two-steps algorithm for min-based possibilistic causal networks. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 266–277. Springer, Heidelberg (2001)
Benferhat, S., Hué, J., Lagrue, S., Rossit, J.: Interval-based possibilistic logic. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16-22, pp. 750–755 (2011)
Benferhat, S., Kaci, S.: Logical representation and fusion of prioritized information based on guaranteed possibility measures: application to the distance-based merging of classical bases. Artif. Intell. 148, 291–333 (2003)
Benferhat, S., Tabia, K.: Three-valued possibilistic networks. In: 20th European Conference on Artificial Intelligence, Montpellier, France, August 27-31, pp. 157–162. IOS Press (2012)
Kruse, R., Borgelt, C., Gebhardt, J.: Possibilistic graphical models. In: International School for the Synthesis of Expert Knowledge (ISSEK 1998), Udine (Italy), pp. 51–68 (1998)
Cozman, F.G.: Credal networks. Artif. Intell. 120(2), 199–233 (2000)
Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press (2009)
de Campos, C.P.: New complexity results for map in bayesian networks. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, IJCAI 2011, Barcelona, Catalonia, Spain, July 16-22, pp. 2100–2106 (2011)
de Campos, C.P., Cozman, F.G.: The inferential complexity of bayesian and credal networks. In: IJCAI 2005, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, Edinburgh, Scotland, UK, July 30-August 5, pp. 1313–1318 (2005)
de Campos, L., Huete, J., Moral, S.: Uncertainty management using probability intervals. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) IPMU 1994. LNCS, vol. 945, pp. 190–199. Springer, Heidelberg (1995)
Dubois, D., Hájek, P., Prade, H.: Knowledge-driven versus data-driven logics. J. of Logic, Lang. and Inf. 9, 65–89 (2000)
Dubois, D., Lang, J., Prade, H.: Timed possibilistic logic. Fundam. Inf. 15, 211–234 (1991)
Guo, P., Tanaka, H.: Decision making with interval probabilities. European Journal of Operational Research 203(2), 444–454 (2010)
Ha, V.A., Doan, A., Vu, V.H., Haddawy, P.: Geometric foundations for interval-based probabilities. Annals of Mathematics and Artificial Intelligence 24, 1–21 (1998)
Hisdal, E.: Conditional possibilities independence and non interaction. Fuzzy Sets and Systems, 283–297 (1978)
Jensen, F.V.: An Introduction to Bayesian Networks. UCL Press, London (1996)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Walley, P.: Statistical reasoning with imprecise probabilities (1991)
Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 100(suppl. 1), 9–34 (1999)
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Benferhat, S., Lagrue, S., Tabia, K. (2014). Interval-Based Possibilistic Networks. In: Straccia, U., Calì, A. (eds) Scalable Uncertainty Management. SUM 2014. Lecture Notes in Computer Science(), vol 8720. Springer, Cham. https://doi.org/10.1007/978-3-319-11508-5_4
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DOI: https://doi.org/10.1007/978-3-319-11508-5_4
Publisher Name: Springer, Cham
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