On the Properties of Probabilistic Implications

  • Przemysław Grzegorzewski
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 107)


A new family of implication operators, called probabilistic implications, are discussed. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that probabilistic fuzzy implications have some interesting properties, especially those connected with the dependence structure of the underlying environment. Therefore, it seems that probabilistic implications might be a useful tool in approximate reasoning, knowledge extraction and decision making.


Fuzzy Logic Tail Dependence Continuous Random Variable Implication Operator Approximate Reasoning 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

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