Conflict Management in Information Fusion with Belief Functions

  • Arnaud MartinEmail author
Part of the Information Fusion and Data Science book series (IFDS)


In information fusion, the conflict is an important concept. Indeed, combining several imperfect experts or sources allows conflict. In the theory of belief functions, this notion has been discussed a lot. 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, and some approaches have been proposed in order to manage this conflict or to decide with conflicting mass functions. We recall in this chapter some of them, and we propose a discussion to consider the conflict in information fusion with the theory of belief functions.


Belief functions Conflict measure Combination rule Reliability Ignorance Decision 


  1. 1.
    A. Appriou, Uncertainty Theories and Multisensor Data Fusion, (ISTE Ltd, UK/Wiley, USA, 2014)Google Scholar
  2. 2.
    M. Chebbah, B. Ben Yaghlane, A. Martin, Reliability estimation based on conflict for evidential database enrichment, in Belief, Brest (2010)Google Scholar
  3. 3.
    M. Chebbah, A. Martin, B. Ben Yaghlane, Combining partially independent belief functions. Decis. Support Syst. 73, 37–46 (2015)CrossRefGoogle Scholar
  4. 4.
    L.Z. Chen, W.K. Shi, Y. Deng, Z.F. Zhu, A new fusion approach based on distance of evidences. J. Zhejiang Univ. Sci. 6A(5), 476–482 (2005)Google Scholar
  5. 5.
    A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 83, 325–339 (1967)MathSciNetCrossRefGoogle Scholar
  6. 6.
    T. Denœux, Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artif. Intell. 172, 234–264 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    S. Destercke, T. Burger, Revisiting the notion of conflicting belief functions, in Belief, Compiègne (2012)Google Scholar
  8. 8.
    J. Dezert, Foundations for a new theory of plausible and paradoxical reasoning. Inf. Secur. Int. J. 9, 13–57 (2002)Google Scholar
  9. 9.
    D. Dubois, H. Prade, Representation and combination of uncertainty with belief functions and possibility measures. Comput. Intell. 4, 244–264 (1988)CrossRefGoogle Scholar
  10. 10.
    Z. Elouedi, K. Mellouli, Ph. Smets, Assessing sensor reliability for multisensor data fusion within the transferable belief model. IEEE Trans. Syst. Man Cybern. B: Cybern. 34(1), 782–787 (2004)CrossRefGoogle Scholar
  11. 11.
    A. Essaid, A. Martin, G. Smits, B. Ben Yaghlane, A distance-based decision in the credal level, in International Conference on Artificial Intelligence and Symbolic Computation (AISC 2014), Sevilla (2014), pp. 147–156Google Scholar
  12. 12.
    M.C. Florea, A.-L. Jousselme, E. Bossé, D. Grenier, Robust combination rules for evidence theory. Inf. Fusion 10, 183–197 (2009)CrossRefGoogle Scholar
  13. 13.
    T. George, N.R. Pal, Quantification of conflict in Dempster-Shafer framework: a new approach. Int. J. Gen. Syst. 24(4), 407–423 (1996)CrossRefGoogle Scholar
  14. 14.
    A.-L. Jousselme, P. Maupin, Distances in evidence theory: comprehensive survey and generalizations. Int. J. Approximate Reason. 53(2), 118–145, (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    A.-L. Jousselme, D. Grenier, E. Bossé, A new distance between two bodies of evidence. Inf. Fusion 2, 91–101 (2001)CrossRefGoogle Scholar
  16. 16.
    G.J. Klir, Measures of uncertainty in the Dempster-Shafer theory of evidence, in Advances in the Dempster-Shafer Theory of Evidence, ed. by R.R. Yager, M. Fedrizzi, J. Kacprzyk (Wiley, New York, 1994), pp. 35–49Google Scholar
  17. 17.
    W. Liu, Analyzing the degree of conflict among belief functions. Artif. Intell. 170, 909–924 (2006)MathSciNetCrossRefGoogle Scholar
  18. 18.
    A. Martin, Comparative study of information fusion methods for sonar images classification, in International Conference on Information Fusion, Philadelphia (2005)Google Scholar
  19. 19.
    A. Martin, Implementing general belief function framework with a practical codification for low complexity, in Advances and Applications of DSmT for Information Fusion, vol. 3 (American Research Press, Rehoboth, 2009), chapter 7, pp. 217–274Google Scholar
  20. 20.
    A. Martin, Reliability and combination rule in the theory of belief functions, in International Conference on Information Fusion (2009), pp. 529–536Google Scholar
  21. 21.
    A. Martin, About conflict in the theory of belief functions, in Belief, Compiègne (2012)Google Scholar
  22. 22.
    A. Martin, C. Osswald, Human experts fusion for image classification. Inf. Secur.: Int. J. Spec. Issue Fusing Uncertain Imprecise Paradoxist Inf. (DSmT) 20, 122–143 (2006)Google Scholar
  23. 23.
    A. Martin, C. Osswald, Toward a combination rule to deal with partial conflict and specificity in belief functions theory, in International Conference on Information Fusion, Québec (2007)Google Scholar
  24. 24.
    A. Martin, I. Quidu, Decision support with belief functions theory for seabed characterization, in International Conference on Information Fusion, Cologne (2008)Google Scholar
  25. 25.
    A. Martin, A.-L. Jousselme, C. Osswald, Conflict measure for the discounting operation on belief functions, in International Conference on Information Fusion, Cologne (2008)Google Scholar
  26. 26.
    D. Mercier, B. Quost, T. Denœux, Refined modeling of sensor reliability in the belief function framework using contextual discounting. Inf. Fusion 9, 246–258 (2006)CrossRefGoogle Scholar
  27. 27.
    C. Murphy, Combining belief functions when evidence conflicts. Decis. Support Syst. 29, 1–9 (2000)CrossRefGoogle Scholar
  28. 28.
    C. Osswald, A. Martin, Understanding the large family of Dempster-Shafer theory’s fusion operators – a decision-based measure, in International Conference on Information Fusion, Florence (2006)Google Scholar
  29. 29.
    C. Rominger, A. Martin, Using the conflict: an application to sonar image registration, in Belief, Brest (2010)Google Scholar
  30. 30.
    G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976)zbMATHGoogle Scholar
  31. 31.
    F. Smarandache, A. Martin, C. Osswald, Contradiction measures and specificity degrees of basic belief assignments, in International Conference on Information Fusion, Boston (2011)Google Scholar
  32. 32.
    Ph. Smets, Constructing the pignistic probability function in a context of uncertainty. Uncertain. Artif. Intell. 5, 29–39 (1990)CrossRefGoogle Scholar
  33. 33.
    Ph. Smets, Analyzing the combination of conflicting belief functions. Inf. Fusion 8(4), 387–412 (2007)CrossRefGoogle Scholar
  34. 34.
    M.J. Wierman, Measuring conflict in evidence theory, in IFSA World Congress and 20th NAFIPS International Conference, vol. 3, no. 21 (2001), pp. 1741–1745Google Scholar
  35. 35.
    R.R. Yager, On the Dempster-Shafer framework and new combination rules. Inf. Sci. 41, 93–137 (1991)MathSciNetCrossRefGoogle Scholar
  36. 36.
    R.R. Yager, On considerations of credibility of evidence. Int. J. Approximate Reason. 7, 45–72 (1992)MathSciNetCrossRefGoogle Scholar
  37. 37.
    L.A. Zadeh, A mathematical theory of evidence (book review). AI Mag. 5, 81–83 (1984)Google Scholar
  38. 38.
    C. Zeng, P. Wu, A reliability discounting strategy based on plausibility function of evidence, in International Conference on Information Fusion, Québec (2007)Google Scholar
  39. 39.
    K. Zhou, A. Martin, Q. Pan, Evidence combination for a large number of sources, in International Conference on Information Fusion, Xian (2017). The paper was acceptedGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.DRUIDUniv Rennes, CNRS, IRISALannionFrance

Personalised recommendations