Sugeno Integral-Based Confidence Intervals for the Theoretical h-Index

  • Marek Gagolewski
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 315)


Sugeno integral-based confidence intervals for the theoretical h-index of a fixed-length sequence of i.i.d. random variables are derived. They are compared with other estimators of such a distribution characteristic in a Pareto i.i.d. model. It turns out that in the first case we obtain much wider intervals. It seems to be due to the fact that a Sugeno integral, which may be applied on any ordinal scale, is known to ignore too much information from cardinal-scale data being aggregated.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Burrell, Q.L.: Hirsch’s h-index: A stochastic model. Journal of Informetrics 1, 16–25 (2007)CrossRefGoogle Scholar
  2. 2.
    Clopper, C., Pearson, E.: The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404–413 (1934)CrossRefzbMATHGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Semantics of quotient operators in fuzzy relational databases. Fuzzy Sets and Systems 78(1), 89–93 (1996)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dubois, D., Prade, H., Testemale, C.: Weighted fuzzy pattern matching. Fuzzy Sets and Systems 28, 313–331 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Franceschini, F., Maisano, D.A.: The Hirsch index in manufacturing and quality engineering. Quality and Reliability Engineering International 25, 987–995 (2009)CrossRefGoogle Scholar
  6. 6.
    Franceschini, F., Maisano, D.A.: Structured evaluation of the scientific output of academic research groups by recent h-based indicators. Journal of Informetrics 5, 64–74 (2011)CrossRefGoogle Scholar
  7. 7.
    Gagolewski, M.: On the relationship between symmetric maxitive, minitive, and modular aggregation operators. Information Sciences 221, 170–180 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gagolewski, M.: Statistical hypothesis test for the difference between hirsch indices of two pareto-distributed random samples. In: Kruse, R., Berthold, M., Moewes, C., Gil, M.A., Grzegorzewski, P., Hryniewicz, O., et al. (eds.) Synergies of Soft Computing and Statistics. AISC, vol. 190, pp. 359–367. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Gągolewski, M., Grzegorzewski, P.: S-statistics and their basic properties. In: Borgelt, C., González-Rodríguez, G., Trutschnig, W., Lubiano, M.A., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O., et al. (eds.) Combining Soft Computing and Statistical Methods in Data Analysis. AISC, vol. 77, pp. 281–288. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Gagolewski, M., Mesiar, R.: Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem. Information Sciences 263, 166–174 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Glänzel, W.: On some new bibliometric applications of statistics related to the h-index. Scientometrics 77(1), 187–196 (2008)CrossRefGoogle Scholar
  12. 12.
    Hirsch, J.E.: An index to quantify individual’s scientific research output. Proceedings of the National Academy of Sciences 102(46), 16569–16572 (2005)CrossRefGoogle Scholar
  13. 13.
    Hovden, R.: Bibliometrics for internet media: Applying the h-index to YouTube. Journal of the American Society for Information Science and Technology 64(11), 2326–2331 (2013)CrossRefGoogle Scholar
  14. 14.
    Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology (1974)Google Scholar
  15. 15.
    Torra, V., Narukawa, Y.: The h-index and the number of citations: Two fuzzy integrals. IEEE Transactions on Fuzzy Systems 16(3), 795–797 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Zieliński, R.: Confidence intervals for proportions (Przedziały ufności dla frakcji). Matematyka Stosowana 10, 51–68 (2009) (in Polish)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

Personalised recommendations