Abstract
In the theory of belief functions, distances between basic belief assignments are very important in many applications like clustering, conflict measuring, reliability estimation. In the discrete domain, many measures have been proposed, however, distance between continuous belief functions have been marginalized due to the nature of these functions. In this paper, we propose an adaptation inspired from the Jousselme’s distance for continuous belief functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dempster, A.P.: Upper and Lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)
Doré, P.E., Martin, A., Abi-Zied, I., Jousselme, A.L., Maupin, P.: Belief functions induced by multimodal probability density functions, an application to search and rescue problem. RAIRO - Operation Research 44(4), 323–343 (2010)
Dubois, D., Prade, H.: The Principle of Minimum Specificity as a basis for Evidential Reasoning. In: Bouchon, B., Yager, R.R. (eds.) Uncertainty in Knowledge-Based Systems. LNCS, vol. 286, pp. 75–84. Springer, Heidelberg (1987)
Hsia, Y.T.: Characterizing belief with minimum commitment. In: International Joint Conference on Artificial Intelligence, IJCAI 1991, pp. 1184–1189. Morgan Kaufman, San Mateo (1991)
Jousselme, A.L., Grenier, D., Bossé, E.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)
Jousselme, A.L., Maupin, P.: On some properties of distances in evidence theory, Belief, Brest, France (2010)
Martin, A., Jousselme, A.L., Osswald, C.: Conflict measure for the discounting operation on belief functions. In: International Conference on Information Fusion, Cologne, Germany (2008)
Nguyen, H.T.: On random sets and belief functions. Journal of Mathematical Analysis and Applications 65, 531–542 (1978)
Ristic, R., Smets, P.: Belief function theory on the continuous space with an application to model based classification, pp. 4–9 (2004)
Ristic, R., Smets, P.: The TBM global distance measure for the association of uncertain combat ID declarations. Information Fusion, 276–284 (2006)
Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)
Smets, P.: Constructing the pignistic probability function in a context of uncertainty. Uncertainty in Artificial Intelligence 5, 29–39 (1990)
Smets, P.: The Combination of Evidence in the Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(5), 447–458 (1990)
Smets, P.: The combination of evidence in the Transferable belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(5), 447–458 (1990)
Smets, P.: Belief Functions on real numbers. International Journal of Approximate Reasoning 40(3), 181–223 (2005)
Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)
Strat, T.: Continuous belief function for evidential reasoning. In: Proceedings of the 4th National Conference on Artificial Intelligence, University of Texas at Austin (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Attiaoui, D., Doré, PE., Martin, A., Ben Yaghlane, B. (2012). A Distance between Continuous Belief Functions. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-33362-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33361-3
Online ISBN: 978-3-642-33362-0
eBook Packages: Computer ScienceComputer Science (R0)