, Volume 105, Issue 3, pp 2089–2108 | Cite as

Mathematical properties of weighted impact factors based on measures of prestige of the citing journals

  • A. Ferrer-SapenaEmail author
  • E. A. Sánchez-Pérez
  • L. M. González
  • F. Peset
  • R. Aleixandre-Benavent


An abstract construction for general weighted impact factors is introduced. We show that the classical weighted impact factors are particular cases of our model, but it can also be used for defining new impact measuring tools for other sources of information—as repositories of datasets—providing the mathematical support for a new family of altmetrics. Our aim is to show the main mathematical properties of this class of impact measuring tools, that hold as consequences of their mathematical structure and does not depend on the definition of any given index nowadays in use. In order to show the power of our approach in a well-known setting, we apply our construction to analyze the stability of the ordering induced in a list of journals by the 2-year impact factor (\(\hbox {IF}_2\)). We study the change of this ordering when the criterium to define it is given by the numerical value of a new weighted impact factor, in which \(\hbox {IF}_2\) is used for defining the weights. We prove that, if we assume that the weight associated to a citing journal increases with its \(\hbox {IF}_2\), then the ordering given in the list by the new weighted impact factor coincides with the order defined by the \(\hbox {IF}_2\). We give a quantitative bound for the errors committed. We also show two examples of weighted impact factors defined by weights associated to the prestige of the citing journal for the fields of MATHEMATICS and MEDICINE, GENERAL AND INTERNAL, checking if they satisfy the “increasing behavior” mentioned above.


Impact factor Weighted Stability Ordering Mathematics Altmetrics 

Mathematics Subject Classification

94A15 94A17 28E99 



The authors want to thank the comments and corrections of the referee, that have improved the contents and presentation of the paper.


  1. Ahlgren, P., & Waltman, L. (2014). The correlation between citation-based and expert-based assessments of publication channels: SNIP and SJR vs. Norwegian quality assessments. Journal of Informetrics, 8, 985–996.CrossRefGoogle Scholar
  2. Aleixandre Benavent, R., Valderrama Zurián, J. C., & González Alcaide, G. (2007). Scientific journals impact factor: Limitations and alternative indicators. El Profesional de la Información, 16(1), 4–11.CrossRefGoogle Scholar
  3. Altmann, K. G., & Gorman, G. E. (1998). The usefulness of impact factor in serial selection: A rank and mean analysis using ecology journals. Library Acquisitions-Practise and Theory, 22, 147–159.CrossRefGoogle Scholar
  4. Arnold, D. N., & Fowler, K. K. (2011). Nefarious numbers. Notices of the American Mathematical Society, 58(3), 434–437.MathSciNetzbMATHGoogle Scholar
  5. Beliakov, G., & James, S. (2012). Using linear programming for weights identification of generalized bonferroni means in R. In: Proceedings of MDAI 2012 modeling decisions for artificial intelligence. Lecture Notes in Computer Science, Vol. 7647, pp. 35–44.Google Scholar
  6. Beliakov, G., & James, S. (2011). Citation-based journal ranks: The use of fuzzy measures. Fuzzy Sets and Systems, 167, 101–119.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Buela-Casal, G. (2003). Evaluating quality of articles and scientific journals. Proposal of weighted impact factor and a quality index. Psicothema, 15(1), 23–25.Google Scholar
  8. Dorta-Gonzalez, P., & Dorta-Gonzalez, M. I. (2013). Comparing journals from different fields of science and social science through a JCR subject categories normalized impact factor. Scientometrics, 95(2), 645–672.CrossRefGoogle Scholar
  9. Dorta-Gonzalez, P., Dorta-Gonzalez, M. I., Santos-Penate, D. R., & Suarez-Vega, R. (2014). Journal topic citation potential and between-field comparisons: The topic normalized impact factor. Journal of Informetrics, 8(2), 406–418.CrossRefGoogle Scholar
  10. Egghe, L., & Rousseau, R. (2002). A general frame-work for relative impact indicators. Canadian Journal of Information and Library Science, 27(1), 29–48.Google Scholar
  11. Gagolewski, M., & Mesiar, R. (2014). Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem. Information Sciences, 263, 166–174.MathSciNetCrossRefGoogle Scholar
  12. Garfield, E. (2006). The history and meaning of the journal impact factor. JAMA, 295(1), 90–93.CrossRefGoogle Scholar
  13. Habibzadeh, F., & Yadollahie, M. (2008). Journal weighted impact factor: A proposal. Journal of Informetrics, 2(2), 164–172.CrossRefGoogle Scholar
  14. Klement, E., Mesiar, R., & Pap, E. (2010). A universal integral as common frame for Choquet and Sugeno integral. IEEE Transaction on Fuzzy System, 18, 178–187.CrossRefGoogle Scholar
  15. Leydesdorff, L., & Opthof, T. (2010). Scopus’s source normalized impact per paper (SNIP) versus a journal impact factor based on fractional counting of citations. Journal of the American Society for Information Science and Technology, 61, 2365–2369.CrossRefGoogle Scholar
  16. Li, Y. R., Radicchi, F., Castellano, C., & Ruiz-Castillo, J. (2013). Quantitative evaluation of alternative field normalization procedures. Journal of Informetrics, 7(3), 746–755.CrossRefGoogle Scholar
  17. Moed, H. F. (2010). Measuring contextual citation impact of scientific journals. Journal of Informetrics, 4, 265–277.CrossRefGoogle Scholar
  18. NISO. (2014). Alternative metrics initiative phase 1. White paper.
  19. Owlia, P., Vasei, M., Goliaei, B., & Nassiri, I. (2011). Normalized impact factor (NIF): An adjusted method for calculating the citation rate of biomedical journals. Journal of Biomedical Informatics, 44(2), 216–220.CrossRefGoogle Scholar
  20. Pinski, G., & Narin, F. (1976). Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics. Information Processing and Management, 12, 297–312.CrossRefGoogle Scholar
  21. Pinto, A. C., & Andrade, J. B. (1999). Impact factor of scientific journals: What is the meaning of this parameter? Quimica Nova, 22, 448–453.CrossRefGoogle Scholar
  22. Raghunathan, M. S., & Srinivas, V. (2001). Significance of impact factor with regard to mathematics journals. Current Science, 80(5), 605.Google Scholar
  23. Ruiz Castillo, J., & Waltman, L. (2015). Field-normalized citation impact indicators using algorithmically constructed classification systems of science. Journal of Informetrics, 9, 102–117.CrossRefGoogle Scholar
  24. Saha, S., Saint, S., & Christakis, D. A. (2003). Impact factor: A valid measure of journal quality? Journal of the Medical Library Association, 91, 42–46.Google Scholar
  25. Torra, V., & Narukawa, Y. (2008). The h-index and the number of citations: Two fuzzy integrals. IEEE Transaction on Fuzzy System, 16, 795–797.MathSciNetCrossRefGoogle Scholar
  26. Torres-Salinas, D., & Jimenez-Contreras, E. (2010). Introduction and comparative study of the new scientific journals citation indicators in journal citation reports and scopus. El Profesional de la Información, 19, 201–207.CrossRefGoogle Scholar
  27. Waltman, L., & van Eck, N. J. (2008). Some comments on the journal weighted impact factor proposed by Habibzadeh and Yadollahie. Journal of Informetrics, 2(4), 369–372.CrossRefGoogle Scholar
  28. Waltman, L., van Eck, N. J., van Leeuwen, T. N., & Visser, M. S. (2013). Some modifications to the SNIP journal impact indicator. Journal of Informetrics, 7, 272–285.CrossRefGoogle Scholar
  29. Zitt, M. (2011). Behind citing-side normalization of citations: some properties of the journal impact factor. Scientometrics, 89, 329–344.CrossRefGoogle Scholar
  30. Zitt, M., & Small, H. (2008). Modifying the journal impact factor by fractional citation weighting: The audience factor. Journal of the American Society for Information Science and Technology, 59, 1856–1860.CrossRefGoogle Scholar
  31. Zyczkowski, K. (2010). Citation graph, weighted impact factors and performance indices. Scientometrics, 85(1), 301–315.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  • A. Ferrer-Sapena
    • 1
    Email author
  • E. A. Sánchez-Pérez
    • 2
  • L. M. González
    • 3
  • F. Peset
    • 1
  • R. Aleixandre-Benavent
    • 4
  1. 1.Instituto de Diseño y FabricaciónUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Instituto Universitario de Matemática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain
  3. 3.F.C.A.F.E.Universidad de ValenciaValenciaSpain
  4. 4.C.S.I.C.ValenciaSpain

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