Measuring Uncertainty for Interval Belief Structures and its Application for Analyzing Weather Forecasts

  • Andrey G. BronevichEmail author
  • Natalia S. Spiridenkova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


While analyzing statistical data we face with a problem of modeling uncertainty. One among well justified models is based on belief structures that allow us to describe imprecision and conflict in information. We use this model for analyzing contradiction in weather forecasts. For this aim we build several measures of contradiction based on the introduced imprecision index and the disjunctive aggregation rule for interval belief structures. We use these characteristics for analyzing weather forecasts.


Interval belief structures Inclusion indices Wasserstein metric Measures of contradiction 


  1. 1.
    Bronevich, A.G., Klir, G.J.: Measures of uncertainty for imprecise probabilities: an axiomatic approach. Int. J. Approximate Reasoning 51, 365–390 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bronevich, A.G., Lepskiy, A.E.: Imprecision indices: axiomatic, properties and applications. Int. J. Gen. Syst. 44(7–8), 812–832 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cuzzolin, F.: \(L_p\)-consonant approximations of belief functions. IEEE Trans. Fuzzy Syst. 22, 420–436 (2014)CrossRefGoogle Scholar
  4. 4.
    Daniel, M.: Belief functions: a revision of plausibility conflict and pignistic conflict. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. Lecture Notes in Computer Science, vol. 8078, pp. 190–203. Springer, Heidelberg (2013)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: A note on measures of specificity for fuzzy sets. Int. J. Gen. Syst. 10(4), 279–283 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. Int. J. Gen. Syst. 12(3), 193–226 (1986)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: Consonant approximations of belief functions. Int. J. Approximate Reasoning 4, 419–449 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dubois, D., Prade, H.: On the combination of evidence in various mathematical frameworks. In: Flamm, J., Luisi, T. (eds.) Reliability Data Collection and Analysis, pp. 213–241. ECSC, EEC, EAFC, Brussels (1992)CrossRefGoogle Scholar
  9. 9.
    Jousselme, A.-L., Maupin, P.: Distances in evidence theory: comprehensive survey and generalizations. Int. J. Approximate Reasoning 5, 118–145 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kantorovich, L.V.: On mass moving. Dokl. Akad. Nauk USSR 37(7–8), 227–229 (1942)Google Scholar
  11. 11.
    Klir, G.J.: Uncertainty and Information: Foundations of Generalized Information Theory. Wiley-Interscience, Hoboken (2006)zbMATHGoogle Scholar
  12. 12.
    Lepskiy, A.E.: About relation between the measure of conflict and decreasing of ignorance in theory of evidence. In: Proceedings of 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013), pp. 355–362. Atlantis Press, Amsterdam, Beijing, Paris (2013)Google Scholar
  13. 13.
    Liu, W.: Analysing the degree of conflict among belief functions. Artif. Intell. 170, 909–924 (2006)CrossRefzbMATHGoogle Scholar
  14. 14.
    Rubner, Y., Tomasi, C., Guibas, L.J.: The Earth mover’s distance as a metric for image retrieval. Int. J. Comput. Vis. 40(2), 99–121 (2000)CrossRefzbMATHGoogle Scholar
  15. 15.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  16. 16.
    Smets, P.: The combination of evidence in the transferable belief model. IEEE Trans. Pattern Anal. Mach. Intell. 12, 447–458 (1990)CrossRefGoogle Scholar
  17. 17.
    Smets, P.: Belief functions on real numbers. Int. J. Approximate Reasoning 40(3), 181–223 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Andrey G. Bronevich
    • 1
    Email author
  • Natalia S. Spiridenkova
    • 1
  1. 1.National Research University Higher School of EconomicsMoscowRussia

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