Advertisement

About Conflict in the Theory of Belief Functions

  • Arnaud Martin
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)

Abstract

In the theory of belief functions, the conflict is an important concept. Indeed, combining several imperfect experts or sources allows conflict. However, the mass appearing on the empty set during the conjunctive combination rule is generally considered as conflict, but that is not really a conflict. Some measures of conflict have been proposed, we recall some of them and we show some counter-intuitive examples with these measures. Therefore we define a conflict measure based on expected properties. This conflict measure is build from the distance-based conflict measure weighted by a degree of inclusion introduced in this paper.

Keywords

Mass Function Information Fusion Combination Rule Belief Function Evidence Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chebbah, M., Ben Yaghlane, B., Martin, A.: Reliability estimation based on conflict for evidential database enrichment. In: Belief, Brest, France (2010)Google Scholar
  2. 2.
    Dempster, A.P.: Upper and Lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 83, 325–339 (1967)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Jousselme, A.-L., Grenier, D., Bossé, E.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)CrossRefGoogle Scholar
  4. 4.
    Jousselme, A.-L., Maupin, P.: On some properties of distances in evidence theory. In: Belief, Brest, France (2010)Google Scholar
  5. 5.
    Jousselme, A.-L., Maupin, P.: Distances in evidence theory: Comprehensive survey and generalizations. International Journal of Approximate Reasoning (2011)Google Scholar
  6. 6.
    Klir, G.J.: Measures of uncertainty in the Dempster-Shafer theory of evidence. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 35–49. John Wiley and Sons, New York (1994)Google Scholar
  7. 7.
    George, T., Pal, N.R.: Quantification of conflict in Dempster-Shafer framework: a new approach. International Journal of General Systems 24(4), 407–423 (1996)zbMATHCrossRefGoogle Scholar
  8. 8.
    Liu, W.: Analyzing the degree of conflict among belief functions. Artificial Intelligence 170, 909–924 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Martin, A., Osswald, C.: Toward a combination rule to deal with partial conflict and specificity in belief functions theory. In: International Conference on Information Fusion, Québec, Canada (2007)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    Osswald, C., Martin, A.: Understanding the large family of Dempster-Shafer theory’s fusion operators - a decision-based measure. In: International Conference on Information Fusion, Florence, Italy (2006)Google Scholar
  12. 12.
    Rominger, C., Martin, A.: Using the conflict: An application to sonar image registration. In: Belief, Brest, France (2010)Google Scholar
  13. 13.
    Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)Google Scholar
  14. 14.
    Smarandache, F., Martin, A., Osswald, C.: Contradiction measures and specificity degrees of basic belief assignments. In: International Conference on Information Fusion, Boston, USA (2011)Google Scholar
  15. 15.
    Smets, P.: Constructing the pignistic probability function in a context of uncertainty. Uncertainty in Artificial Intelligence 5, 29–39 (1990)Google Scholar
  16. 16.
    Smets, P.: Analyzing the combination of conflicting belief functions. Information Fusion 8(4), 387–412 (2007)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wierman, M.J.: Measuring Conflict in Evidence Theory. In: IFSA World Congress and 20th NAFIPS International Conference, vol. 3(21), pp. 1741–1745 (2001)Google Scholar
  18. 18.
    Yager, R.R.: Entropy and Specificity in a Mathematical Theory of Evidence. International Journal of General Systems 9, 249–260 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Yager, R.R.: On Considerations of Credibility of Evidence International. Journal of Approximate Reasoning 7, 45–72 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Zadeh, L.A.: A mathematical theory of evidence (book review). AI Magazine 5, 81–83 (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.University of Rennes 1, IRISALannionFrance

Personalised recommendations