Ranking of qualitative decision options using copulas

  • Biljana Mileva-Boshkoska
  • Marko Bohanec
Conference paper
Part of the Operations Research Proceedings book series (ORP)


We study the ranking of classified multi-attribute qualitative options. To obtain a full ranking of options within classes, qualitative options are mapped into quantitative ones. Current approaches, such as the Qualitative-Quantitative (QQ) method, use linear functions for ranking, hence performing well for linear and monotone options; however QQ underperforms in cases of non-linear and nonmonotone options. To address this problem, we propose a new QQ-based method in which we introduce copulas as an aggregation utility instead of linear functions. In addition, we analyze the behavior of different hierarchical structures of bivariate copulas to model the non-linear dependences among attributes and classes.


Archimedean Copula Linear Regression Function Clayton Copula Copula Family Inverse Cumulative Distribution Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berg, D., Aas, K.: Models for construction of multivariate dependance: A comparison study. European Journal of Finance 15(7-8), 639–659 (2009)Google Scholar
  2. 2.
    Bohanec, M.: Odloˇcanje in modeli. DMFA, Ljubljana (2006) 3. Bohanec, M.: DEXi: Program for Multi-Attribute Decision Making: User’s manual : versionGoogle Scholar
  3. 3.
    3.03. IJS Report DP-10707, Joˇzef Stefan Institute, Ljubljana (2011)Google Scholar
  4. 4.
    Bohanec, M., Rajkoviˇc, V.: DEX: An expert system shell for decision support. Sistemica 1, 145–157 (1990)Google Scholar
  5. 5.
    Bohanec, M., Urh, B., Rajkoviˇc, V.: Evaluation of options by combined qualitative and quantitative methods. Acta Psychologica 80, 67–89 (1992)CrossRefGoogle Scholar
  6. 6.
    Bouy´e, E., Salmon, M.: Dynamic copula quantile regressions and tail area dynamic dependence in forex markets. European Journal Of Finance 15, 721–750 (2009)Google Scholar
  7. 7.
    Brown, L., Cai, T., Zhang, R., Zhao, L., Zhou, H.: A root-unroot transform and wavelet block thresholding approach to adaptive density estimation. unpublished (2005)Google Scholar
  8. 8.
    Fischer, M., Kock, C., Schluter, S., Weigert, F.: An empirical analysis of multivariate copula models. Quantitative Finance 9(7), 839–854 (2009)CrossRefGoogle Scholar
  9. 9.
    Joe, H.: Multivariate Models and Dependence Consepts. Chapman and Hall (1997)Google Scholar
  10. 10.
    Kolev, N., Paiva, D.: Copula based regression models: A survey. Journal of Statistical Planning and Inference 139(11), 3847 – 3856 (2009)CrossRefGoogle Scholar
  11. 11.
    Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)Google Scholar
  12. 12.
    Savu, C., Trade, M.: Hierarchical archimedean copulas. In: International Conference on High Frequency Finance. Konstanz, Germany (2006)Google Scholar
  13. 13.
    Trivedi, P., David, Z.: Copula Modeling: An Introduction for Practitioners. World Scientific Publishing (2006)Google Scholar
  14. 14.
    Wasserman, L.: All of Nonparametric Statistics. Springer Texts in Statistics, USA (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Jožef Stefan InstituteLjubljanaSlovenia
  2. 2.University of Nova GoricaNova GoricaSlovenia

Personalised recommendations