Abstract
This paper is a self-contained presentation of a method for combining several belief functions on a common frame that is different from a mere application of Dempster’s rule. All the necessary results and their proofs are presented in the paper. It begins with a review and explanation of concepts related to the notion of non-normalized mass-function, or gem-function, introduced by P. Smets under the name basic belief assignment [1,6]. Then the link with Dempster’s rule of combination is established. Several results in relation with the notion of Dempster specialization matrix are proved for the first time [2]. Based on these results, the method is then presented and a small application is considered.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. Smets. The Nature of the Unnormalized Beliefs Encountered in the Transferable Belief Model. In Dubois D., Wellman M., D’Ambrosio B., and Smets P., editors, Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence, pages 292–297. Morgan Kaufman Publishers, San Francisco, California, 1992.
P. Smets. The Transferable Belief Model for Quantified Belief Representation. In Smets P. (Ed.) Quantified Representation of Uncertainty and Imprecision. Volume 1 in the Series Gabbay D., Smets P. (Eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, pages 267–301. Kluwer Academic Publishers, 1998.
F. Klawonn and P. Smets. The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices. In Dubois D., Wellman M., D’Ambrosio B., and Smets P., editors, Proceedings of the8th Conference on Uncertainty in Artificial Intelligence, pages 130–137. Morgan Kaufman Publishers, San Francisco, California, 1992.
G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, 1976.
J. Kohlas and P.A. Monney. A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence, volume 425 of Lecture Notes in Economics and Mathematical Systems. Springer Verlag, 1995.
P. Smets. The Combination of Evidence in the Transferable Belief Model. IEEE Trans. PAMI, 12:447–458, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Monney, PA. (2001). Dempster Specialization Matrices and the Combination of Belief Functions. In: Benferhat, S., Besnard, P. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Lecture Notes in Computer Science(), vol 2143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44652-4_28
Download citation
DOI: https://doi.org/10.1007/3-540-44652-4_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42464-2
Online ISBN: 978-3-540-44652-1
eBook Packages: Springer Book Archive