On the behavior of Dempster's rule of combination and the foundations of Dempster-Shafer Theory

IS'2012 - 2012 6th IEEE International Conference Intelligent Systems, Proceedings

Volumn , Issue , 2012, Pages 108-113

  Tchamova, Albena ^a   Dezert, Jean ^b  

^a INSTITUTE OF INFORMATION AND COMMUNICATION TECHNOLOGIES   (Bulgaria)

^b ONERA   (France)

Author keywords

Belief functions; contradiction; Dempster Shafer Theory; DSmT; PCR5

Indexed keywords

BELIEF FUNCTION; CONTRADICTION; DEMPSTER-SHAFER THEORY; DSMT; PCR5;

UNCERTAINTY ANALYSIS;

INTELLIGENT SYSTEMS;

EID: 84869829126     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IS.2012.6335122     Document Type: Conference Paper

References (20)

1. Shafer, G. A Mathematical Theory of Evidence. Princeton University Press, Princeton, 1976.
2. Dempster, A. Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Statist., Vol. 38, 1967, pp. 325-339.
3. Dempster, A. A generalization of Bayesian inference, J. R. Stat. Soc. B 30, 1968, pp. 205-247.
4. Dempster, A. The Dempster-Shafer calculus for statisticians, IJAR, Vol. 48, 2008, pp. 365-377.
5. Smets, P. Practical uses of belief functions. in K. B. Lskey and H. Prade, Editors, UAI 99, Stockholm, Sweden, 1999, pp. 612-621.
6. Zadeh, L. A. On the validity of Dempster's rule of combination, Memo M79/24, Univ. of California, Berkeley, U. S. A., 1979.
7. Zadeh, L. A. Book review: A mathematical theory of evidence, The Al Magazine, Vol. 5 (3), 1984, pp. 81-83.
8. Zadeh, L. A. A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination, The Al Magazine, Vol. 7 (2), 1986, pp. 85-90.
9. Lemmer, J. Confidence factors, empiricism and the Dempster-Shafer theory of evidence, Proc. of 1st Conf. on UAI, 1985, pp. 160-176.
10. Voorbraak, F. On the justification of Demspster's rule of combination, Utrecht Univ., Netherlands, Logic Group Preprint Series, No. 42, 1988.
11. Wang, P. A defect in Dempster-Shafer theory, in Proc. of 10th Conf. on Uncertainty in AI, 1994, pp. 560-566.
12. Pearl, J. Reasoning with belief functions: An analysis of compatibility, Int. Journal of Approximate Reasoning, Vol. 4, 1990, pp. 363-389.
13. Walley, P. Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London, 1991, pp. 278-281.
14. Gelman, A. The boxer, the wrestler, and the coin flip: a paradox of robust Bayesian inference and belief functions, American Statistician, Vol. 60, No. 2, 2006, pp. 146-150.
15. Smarandache F., Dezert J. Advances and applications of DSmT for information fusion, Volumes 1, 2 & 3, ARP, 2004-2009 (http://www. gallup. unm. edu/̃smarandache/DSmT. htm).
16. Smets P., Kennes R. The transferable belief model, Artif. Int., Vol. 66, 1994, pp. 191-234.
17. Smets, P. The transferable belief model for quantified belief representation, Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1, Kluwer, 1998.
18. Dezert J., Tchamova A. On the behavior of Dempster's rule of combination, School on Belief Functions Theory and Applications, Autrans, France, 4-8 April 2011 (http://hal. archives-ouvertes. fr/hal-00577983/).
19. Dezert J., Tchamova A., Dambreville F. On the mathematical theory of evidence and Dempster's rule of combination, May 2011 (http://hal. archives-ouvertes. fr/hal-00591633/fr/).
20. Dezert J., Wang P., Tchamova A. On The Validity of Dempster-Shafer Theory, Proc. of 15th Int. Conf. of Information Fusion, July 9-12, 2012.