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Abstract

Recently, fuzzy implications based on copulas, i.e. probabilistic implications and probabilistic S-implications, were introduced and their properties were explored. However, the reverse problem of copulas derived from fuzzy implications, suggested by Massanet et al. [11, 12], is also of interest. In the paper we consider geometric properties of those fuzzy implications that generate copulas. Moreover, we consider the reverse problem for some generalizations of copulas like quasi-copulas and semi-copulas.

Keywords

Copula Fuzzy implication Probabilistic implication Spearman’s rho Diagonal section Quasi-copula Semi-copula 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Systems Research Institute, Polish Academy of SciencesWarsawPoland
  2. 2.Faculty of Mathematics and Computer ScienceWarsaw University of TechnologyWarsawPoland

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