The Fuzzy Representation of Prior Information for Separating Outliers in Statistical Experiments

  • Dmitry A. MatsypaevEmail author
  • Andrey G. Bronevich
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 315)


The paper presents a new fuzzy set based description which helps to distinguish the expected values of the statistical experiment from the outliers. Since the Neyman-Pearson criterion is not adequate in some real applications for such purpose, we propose to use triangular norms for conjuction of two propositions about typical and non-typical values and describe both of them as a fuzzy set that is called the typical transform. We also investigate such a property of the typical transform as stability.


distortion function triangular norm fuzzy set Neyman-Pearson criterion outliers Lipschitz continuity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bronevich, A.G., Karkishchenko, A.N.: Statistical classes and fuzzy set theoretical classification of probability distributions. In: Statistical Modeling, Analysis and Management of Fuzzy Data, pp. 173–198. Physica-Verl., Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Chateauneuf, A.: Decomposable capacities, distorted probabilities and concave capacities. Mathematical Social Sciences 31, 19–37 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Fuzzy sets and probability: misunderstandings, bridges and gaps In. In: Proc. of the Second IEEE Conderence on Fuzzy Systems, pp. 1059–1068. IEEE (1993)Google Scholar
  4. 4.
    Hodge, V.J., Austin, J.: A survey of outlier detection methodologies. Artificial Intelligence Review 22(2), 85–126 (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular norms, 1st edn., p. 387. Springer, Heidelberg (2000)CrossRefzbMATHGoogle Scholar
  6. 6.
    Mesiarova, A.: Triangular norms and k-Lipschitz property. In: EUSFLAT Conf., pp. 922–926 (2005)Google Scholar
  7. 7.
    Wallner, A.: Bi-elastic neighbourhood models. In: Proc. of the 3rd International Symposium on Imprecise Probabilities and Their Applications, Lugano, Switzerland, pp. 591–605 (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Southern Federal UniversityTaganrogRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia

Personalised recommendations