A class of extended aggregation operators, called impact functions, is proposed and their basic properties are examined. Some important classes of functions like generalized ordered weighted averaging (OWA) and ordered weighted maximum (OWMax) operators are considered. The general idea is illustrated by the Producer Assessment Problem which includes the scientometric problem of rating scientists basing on the number of citations received by their publications. An interesting characterization of the well known h-index is given.


aggregation extended aggregation function OWA OWMax h-index scientometrics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arrow, K.J.: A difficulty in the concept of social welfare. Journal of Political Economy 58(4), 328–346 (1950)CrossRefGoogle Scholar
  2. 2.
    Benjamini, Y., Hochberg, Y.: Controlling false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B 57(1), 289–300 (1995)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Calvo, T., Kolesarova, A., Komornikova, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators. New Trends and Applications, Studies in Fuzziness and Soft Computing, vol. 97, pp. 3–104. Physica-Verlag, New York (2002)CrossRefGoogle Scholar
  4. 4.
    Calvo, T., Mayor, G.: Remarks on two types of extended aggregation functions. Tatra Mountains Mathematical Publications 16, 235–253 (1999)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Dubois, D., Prade, H., Testemale, C.: Weighted fuzzy pattern matching. Fuzzy Sets and Systems 28, 313–331 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Grabisch, M., Pap, E., Marichal, J.L., Mesiar, R.: Aggregation Functions, Cambridge (2009)Google Scholar
  7. 7.
    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
  8. 8.
    Marchant, T.: An axiomatic characterization of the ranking based on the h-index and some other bibliometric rankings of authors. Scientometrics 80(2), 325–342 (2009)CrossRefGoogle Scholar
  9. 9.
    Marchant, T.: Score-based bibliometric rankings of authors. Journal of the American Society for Information Science and Technology 60(6), 1132–1137 (2009)CrossRefGoogle Scholar
  10. 10.
    May, K.O.: A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20(4), 680–684 (1952)CrossRefzbMATHGoogle Scholar
  11. 11.
    Mayor, G., Calvo, T.: On extended aggregation functions. In: Proc. IFSA 1997, vol. 1, pp. 281–285. Academia, Prague (1997)Google Scholar
  12. 12.
    Palacios-Huerta, I., Volij, O.: The measurement of intellectual influence. Econometrica 72(3), 963–977 (2004)CrossRefzbMATHGoogle Scholar
  13. 13.
    Torra, V. (ed.): Information Fusion in Data Mining. Studies in Fuzziness and Soft Computing, vol. 123. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  14. 14.
    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
  15. 15.
    Woeginger, G.J.: An axiomatic analysis of Egghe’s g-index. Journal of Informetrics 2(4), 364–368 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Woeginger, G.J.: An axiomatic characterization of the Hirsch-index. Mathematical Social Sciences 56(2), 224–232 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multictriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics 18(1), 183–190 (1988)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

Personalised recommendations