Plausibility in DSmT

Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)


Preparing for generalization of results on conflicts of classic belief function to DSm approach, we need normalized plausibility of singletons also in DSmT. To enable this, plausibility of DSm generalized belief functions is analyzed and compared on entire spectrum of DSm models for various types of belief functions; from simple uniform distribution, through general classic belief function, to general generalized belief function in full generality. Both numeric and comparative variability with respect to particular DSm models has been observed and described. This comparative study enables deeper understanding of plausibility in DSm approach and also underlines the sensitivity to selection of particular DSm models.

Figure of elements of DSm domain—DSm hyper-power set—and figures representing particular DSm models (the free DSm model, hybrid DSm models, and Shafer’s model) throughout the text enable better understanding of DSm principles.

Further, a notion of non-conflicting DSm model is introduced and characterized towards the end of the study.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cholvy, L.: Using Logic to Understand Relations between DSmT and Dempster-Shafer Theory. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS(LNAI), vol. 5590, pp. 264–274. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Daniel, M.: A Generalization of the Classic Combination Rules to DSm Hyper-power Sets. Information & Security. An International Journal 20, 50–64 (2006)MathSciNetGoogle Scholar
  3. 3.
    Daniel, M.: The DSm Approach as a Special Case of the Dempster-Shafer Theory. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 381–392. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Daniel, M.: Contribution of DSm Approach to the Belief Function Theory. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proc. of IPMU 2008, Málaga, pp. 417–424 (2008)Google Scholar
  5. 5.
    Daniel, M.: Conflicts within and between Belief Functions. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS(LNAI), vol. 6178, pp. 696–705. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Daniel, M.: Non-conflicting and Conflicting Parts of Belief Functions. In: Coolen, F., de Cooman, G., Fetz, T., Oberguggenberger, M. (eds.) Proceedings of the 7th ISIPTA 2011, pp. 149–158. Studia Universitätsverlag, Innsbruck (2011)Google Scholar
  7. 7.
    Dezert, J.: Foundations for a New Theory of Plausible and Paradoxical Reasoning. Information and Security, An International Journal 9 (2002)Google Scholar
  8. 8.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton Univ. Press, New Jersey (1976)MATHGoogle Scholar
  9. 9.
    Smarandache, F., Dezert, J.: Advances and Applications of DSmT for Information Fusion. American Research Press, Rehoboth (2004)MATHGoogle Scholar
  10. 10.
    Smarandache, F., Dezert, J.: Advances and Applications of DSmT for Information Fusion, vol. 2. American Research Press, Rehoboth (2006)MATHGoogle Scholar
  11. 11. (cited, January 28, 2012)

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

Personalised recommendations