Abstract
Given a number of Dempster-Shafer belief functions there are different architectures which allow to do a compilation of the given knowledge. These architectures are the Shenoy-Shafer Architecture, the Lauritzen-Spiegelhalter Architecture and the HUGIN Architecture. We propose a new architecture called “Fast-Division Architecture” which is similar to the former two. But there are two important advantages: (i) results of intermediate computations are always valid Dempster-Shafer belief functions and (ii) some operations can often be performed much more efficiently.
Research supported by grant No. 2100-042927.95 of the Swiss National Foundation for Research.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Almond, R.G. 1990. Fusion and Propagation of Graphical Belief Models: an Implementation and an Example. Ph.D. thesis, Department of Statistics, Harvard University.
Bissig, R. 1996. Eine schnelle Divisionsarchitektur für Belief-Netwerke. M.Phil. thesis, Institute of Informatics, University of Fribourg.
Dugat, V., & Sandri, S. 1994. Complexity of Hierarchical Trees in Evidence Theory. ORSA Journal on Computing, 6, 37–49.
F.V. Jensen, S.L. Lauritzen, & Olesen, K.G. 1990. Bayesian Updating in Causal Probabilistic Networks by Local Computations. Computational Statistics Quarterly, 4, 269–282.
Kennes, R., & Smets, P. 1990. Computational Aspects of the Möbius Transform. Pages 344–351 of: Proceedings of the 6th Conference on Uncertainty in Artificial Intelligence.
Kohlas, J., & Monney, P.A. 1995. A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems, vol. 425. Springer.
Lauritzen, S.L., & Spiegelhalter, D.J. 1988. Local Computations with Probabil-ities on Graphical Structures and their Application to Expert Systems. J. R. Statist Soc. B, 50(2), 157–224.
Pearl, J. 1986. Fusion, Propagation and Structuring in Belief Networks. Artificial Intelligence, Elsevier Science Publisher B. V. (Amsterdam), 329, 241–288.
Saffiotti, A., & Umkehrer, E. 1991. PULCINELLA: A General Tool for Propa-gating Uncertainty in Valuation Networks. Tech. Rep. IRIDIA, Université de Bruxelles.
Shafer, G. 1976. A Mathematical Theory of Evidence. Princeton University Press.
Shenoy, P.P. 1989. A Valuation-Based Language for Expert Systems. International Journal of Approximate Reasoning, 3, 383–411.
Shenoy, P.P., & Shafer, G. 1990. Axioms for Probability and Belief-Functions Propagation. In: R.D. Shachter, T.S. Levitt, L.N. Kanal (ed), Uncertainty in Artificial Intelligence 4. Elsevier Science Publishers B.V.
Smets, Ph. 1988. Belief Functions. Pages 253–286 of: Ph. Smets, A. Mamdani, D. Dubois, & Prade, H. (eds), Nonstandard logics for automated reasoning. Academic Press.
Thoma, H. Mathis. 1991. Belief Function Computations. Pages 269–307 of: I.R. Goodman, M.M. Gupta, H.T. Nguyen, & Rogers, G.S. (eds), Conditional Logic in Expert Systems. Elsevier Science.
Xu, H., & Kennes, R. 1994. Steps toward efficient implementation of Dempster-Shafer theory. Pages 153–174 of: Yager, R.R., Kacprzyk, J., & Fedrizzi, M. (eds), Advances in the Dempster-Shafer Theory of Evidence. Wiley.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bissig, R., Kohlas, J., Lehmann, N. (1997). Fast-division architecture for Dempster-Shafer belief functions. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds) Qualitative and Quantitative Practical Reasoning. FAPR ECSQARU 1997 1997. Lecture Notes in Computer Science, vol 1244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035623
Download citation
DOI: https://doi.org/10.1007/BFb0035623
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63095-1
Online ISBN: 978-3-540-69129-7
eBook Packages: Springer Book Archive