The Theoretical Methods of Constructing Fuzzy Inference Relations

  • Xiao-Ning Wang
  • Xue-Hai Yuan
  • Hong-Xing Li
Part of the Advances in Soft Computing book series (AINSC, volume 54)


In this paper, a theoretical method of selecting fuzzy implication operators for the fuzzy inference sentence as “if x is A, then y is B” is presented. By applying representation theorems, thirty-two fuzzy implication operators are obtained. It is shown that the thirty-two fuzzy implication operators are generalizations of classical inference rule AB, A c B, AB c and A c B c respectively and can be divided four classes. By discussion, it is found that thirty fuzzy implication operators among 420 fuzzy implication operators presented by Li can be derived by applying representation theorems and two new fuzzy implication operators are obtained by the use of our methods.


Fuzzy Set Cut Set Representation Theorem Fuzzy Inference Implication Operator 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Xiao-Ning Wang
    • 1
  • Xue-Hai Yuan
    • 2
  • Hong-Xing Li
    • 2
  1. 1.School of MathematicsLiaoning Normal UniversityDalianChina
  2. 2.School of Electronic and Information EngineeringDalian University of TechnologyDalianP.R. China

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