Propagation of Belief Functions in Singly-Connected Hybrid Directed Evidential Networks

  • Wafa LaâmariEmail author
  • Boutheina Ben Yaghlane
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9310)


Directed evidential networks (DEVNs) can be seen, at present, as an extremely powerful graphical tool for representing and reasoning with uncertain knowledge in the framework of evidence theory.

The main purpose of this paper is twofold. Firstly, it introduces hybrid directed evidential networks which generalize the standard DEVNs. Secondly, it presents an algorithm for performing inference over singly-connected hybrid evidential networks.


Evidence Network Conditional Belief Functions Conditionals Specified Generalized Bayesian Theorem (GBT) Child Nodes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ben Yaghlane, B., Mellouli, K.: Inference in directed evidential networks based on the transferable belief model. IJAR 48(2), 399–418 (2008)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Ban Yaghlane, B., Mellouli, K.: Updating directed belief networks. In: Hunter, A., Parsons, S. (eds.) ECSQARU 1999. LNCS (LNAI), vol. 1638, pp. 43–54. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  3. 3.
    Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Laâmari, W., Ben Yaghlane, B.: Reasoning in singly-connected directed evidential networks with conditional beliefs. In: Likas, A., Blekas, K., Kalles, D. (eds.) SETN 2014. LNCS, vol. 8445, pp. 221–236. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  5. 5.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)Google Scholar
  6. 6.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976) zbMATHGoogle Scholar
  7. 7.
    Shenoy, P.P.: Valuation networks and conditional independence. In: Uncertainty in Artificial Intelligence, pp. 191–199 (1993)Google Scholar
  8. 8.
    Smets, Ph.: Belief function: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approx. Reasoning 9, 1–35 (1993)Google Scholar
  9. 9.
    Smets, Ph., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–234 (1994)Google Scholar
  10. 10.
    Xu, H., Smets, Ph.: Evidential reasoning with conditional belief functions. In: Heckerman, D., et al. (eds.) Proceedings of Uncertainty in Artificial Intelligence (UAI 1994), pp. 598–606. Morgan Kaufmann, San Mateo (1994)Google Scholar
  11. 11.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LARODEC Laboratory - Institut Supérieur de Gestion de TunisTunisTunisia

Personalised recommendations