Object-oriented algorithm for combining dichotomic belief functions

  • Wagner Teixeira da Silva
  • Pedro Antônio Dourado de Rezende
Logic Programming, Temporal Reasoning and Belief Functions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1159)


The problem of combining dichotomic belief functions over a hierarchical structure of propositions can be viewed as a problem of updating local data in objects and exchanging messages among objects. Such approach is proposed in this paper. A set of propositions is given in a hierarchical structure so that each node represents a proposition. Nodes in the same level represent disjunctive propositions. A node proposition is given by the union of its node proposition children. Evidences for and against propositions in the hierarchy are translated into dichotomic belief functions. In this form they are combined and propagated to and over nodes of the hierarchy. In this approach, each node is an object. There are three classes of objects: root, internal and external nodes. The objects can receive message, update their local data and send messages to their father and children. For each piece of evidence, the effort to combine and propagate has time complexity linearly proportional to the number of propositions and to the branch factor of the hierarchical tree.


Artificial intelligence Knowledge representation Dempster-Shafer theory, dichotomic belief functions Hierarchy of propositions Object-oriented Algorithms 


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  1. BARNETT, J.A. Computational methods for a mathematical theory of evidence. In: Proceedings IJCAI-81, Vancouver, BC, 1981. pp 868–75.Google Scholar
  2. BOOCH, G. Object-Oriented Development. IEEE Transaction on Software Engineering, 12(2):211–21, Feb. 1986.Google Scholar
  3. BOOCH, G. Object Oriented Design: with applications. Menlo Park, CA: Benjamim/ Cummings, 1994.Google Scholar
  4. DEMPSTER, A. P. A generalization of bayesian inference. Journal of Royal Statistical Society, Series B, 30:205–47, 1968.Google Scholar
  5. NGUYEN, Van et alii. A generalized Object Model. ACM SIGPLAN Notices, 21(10):78–87, Oct. 1988.Google Scholar
  6. Shafer, G. A mathematical theory of evidence. Princeton University Press, 1976.Google Scholar
  7. SHAFER, G. & LOGAN, R. Implementing Dempster's Rule for hierarchical evidence. Artificial Intelligence, 33:271–98, 1987.Google Scholar
  8. SHAFER, G., SHENOY, P.P. & MELLOULI, K. Propagating Belief Functions in Qualitative Markov Trees. International Journal of Approximate Reasoning, 1987, 1:349–400.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Wagner Teixeira da Silva
  • Pedro Antônio Dourado de Rezende

There are no affiliations available

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