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Convergence of Intuitionistic Fuzzy Observables

  • Katarína ČunderlíkováEmail author
  • Beloslav Riečan
Conference paper
  • 6 Downloads
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1081)

Abstract

In the paper the space of observables with respect to a family of intuitionistic fuzzy events is considered. Two important theorems are proved: the Central limit theorem and the Strong law of large numbers. They are a basis for statistical applications. As a consequence the corresponding results for fuzzy events are obtained.

Keywords

Intuitionistic fuzzy state Sequence of intuitionistic fuzzy observables Convergence in distribution \(\mathbf {m}\)-almost everywhere convergence Central limit theorem Strong law of large numbers 

References

  1. 1.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications. Studies in Fuzziness and Soft Computing. Physica-Verlag, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Atanassov, K.T.: On Intuitionistic Fuzzy Sets. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Bartková, R., Čunderlíková, K.: About Fisher-Tippett-Gnedenko theorem for intuitionistic fuzzy events. In: Kacprzyk, J., et al. (eds.) Advances in Fuzzy Logic and Technology 2017, IWIFSGN 2017, EUSFLAT 2017. Advances in Intelligent Systems and Computing, vol. 641, pp. 125–135. Springer, Cham (2018)Google Scholar
  4. 4.
    Lendelová, K.: Convergence of IF-observables. In: Issues in the Representation and Processing of Uncertain and Imprecise Information - Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized nets, and Related Topics, pp. 232–240 (2005)Google Scholar
  5. 5.
    Lendelová, K.: Conditional IF-probability. In: Lawry, J., et al. (eds.) Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, pp. 275–283. Springer, Heidelberg (2006)Google Scholar
  6. 6.
    Riečan, B.: On the probability and random variables on IF events. In: Ruan, D., et al. (eds.) Applied Artificial Intelligence, Proceedings of the 7th FLINS Conference, Genova, pp. 138–145 (2006)Google Scholar
  7. 7.
    Riečan, B.: Analysis of fuzzy logic models. In: Koleshko, V. (ed.) Intelligent Systems, INTECH, pp. 219–244 (2012)Google Scholar
  8. 8.
    Riečan, B., Neubrunn, T.: Integral, Measure and Ordering. Kluwer, Dordrecht (1997)CrossRefGoogle Scholar
  9. 9.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–358 (1965)CrossRefGoogle Scholar
  10. 10.
    Zadeh, L.A.: Probability measures on fuzzy sets. J. Math. Anal. Appl. 23, 421–427 (1968)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Mathematical Institute, Slovak Academy of SciencesBratislavaSlovakia

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