An Interval-Valued Dissimilarity Measure for Belief Functions Based on Credal Semantics

  • Alessandro AntonucciEmail author
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)


Evidence theory extends Bayesian probability theory by allowing for a more expressive model of subjective uncertainty. Besides standard interpretation of belief functions, where uncertainty corresponds to probability masses which might refer to whole subsets of the possibility space, credal semantics can be also considered. Accordingly, a belief function can be identified with the whole set of probability mass functions consistent with the beliefs induced by the masses. Following this interpretation, a novel, set-valued, dissimilarity measure with a clear behavioral interpretation can be defined. We describe the main features of this new measure and comment the relation with other measures proposed in the literature.


Mass Function Dissimilarity Measure Probability Mass Function Belief Function Manhattan Distance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abéllan, J., Gómez, M.: Measures of divergence on credal sets. Fuzzy Sets and Systems 157, 1514–1531 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Cuzzolin, F.: On the Credal Structure of Consistent Probabilities. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 126–139. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    de Campos, L.M., Bolaños, M.J.: Characterization of fuzzy measures through probabilities. Fuzzy Sets and Systems 31, 23–36 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Dempster, A.: Upper and lower probabilities induced by multi-valued mapping. Ann. Math. Stat. 38, 325–339 (1967)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Jousselme, A.L., Maupin, P.: Distances in evidence theory: Comprehensive survey and generalizations. International Journal of Approximate Reasoning 53, 118–145 (2012)CrossRefGoogle Scholar
  6. 6.
    Liu, Z., Dezert, J., Pan, Q.: A new measure of dissimilarity between two basic belief assignments. In: Proceedings of Fusion 2010. IEEE (2010)Google Scholar
  7. 7.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)Google Scholar
  8. 8.
    Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.IDSIA, Istituto Dalle Molle di Studi sull’Intelligenza ArtificialeManno-LuganoSwitzerland

Personalised recommendations