In [7] Fredricks et al. showed that certain Iterated Function Systems (IFS) can be used to construct copulas with fractal support. Since, firstly, the same construction also works with respect to the D 1-metric on the space of copulas which is much stronger than the uniform metric and, secondly, the star product of copulas is (jointly) continuous with respect to this metric the IFS approach can also be used to construct idempotent copulas with fractal support. The main result of the paper is that for each open interval I ⊆ [1,2] there exists an idempotent copula A such that the Hausdorff dimension of the support of A is contained in the interval I.


Copula Star product Idempotence Iterated Function System Fractal 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wolfgang Trutschnig
    • 1
  1. 1.Research Unit for Intelligent Data Analysis and Graphical ModelsEuropean Centre for Soft Computing, Edificio de InvestigaciónMieresSpain

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