S-Statistics and Their Basic Properties

  • Marek Gągolewski
  • Przemysław Grzegorzewski
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 77)


Some statistical properties of the so-called S-statistics, which generalize the ordered weighted maximum aggregation operators, are considered. In particular, the asymptotic normality of S-statistics is proved and some possible applications in estimation problems are suggested.


Aggregation L-statistics OWA OWMax operators 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dubois, D., Prade, H.: Weighted minimum and maximum operations in fuzzy set theory. Inform. Sci. 39, 205–210 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dubois, D., Prade, H., Testemale, C.: Weighted fuzzy pattern matching. Fuzzy Sets Syst. 28, 313–331 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Gągolewski, M., Grzegorzewski, P.: Arity-monotonic extended aggregation operators. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) Proceedings of the 13th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2010. Dortmund, Germany. Part I, CCIS, vol. 80, pp. 693–702 (2010)Google Scholar
  4. 4.
    Gągolewski, M., Grzegorzewski, P.: Possibilistic extension of some aggregation operators (submitted for publication, 2010)Google Scholar
  5. 5.
    Grabisch, M., Pap, E., Marichal, J.L., Mesiar, R.: Aggregation Functions. Cambridge University Press, New York (2009)zbMATHGoogle Scholar
  6. 6.
    Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58(301), 13–30 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Serfling, R.J.: Approximation Theorems of Mathematical Statistics. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons Inc., New York (1980)zbMATHCrossRefGoogle Scholar
  8. 8.
    Shevtsova, I.G.: Sharpening of the upper bound of the absolute constant in the Berry-Esseen inequality. Theor. Probab. Appl. 51(3), 549–553 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Torra, V., Narukawa, Y.: The h-index and the number of citations: two fuzzy integrals. IEEE Trans. Fuzzy Syst. 16(3), 795–797 (2008)CrossRefMathSciNetGoogle Scholar
  10. 10.
    van der Vaart, A.W.: Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (2000)Google Scholar
  11. 11.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marek Gągolewski
    • 1
    • 2
  • Przemysław Grzegorzewski
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

Personalised recommendations