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Properties and Relations Between Implication Operators

  • Jiaxin Han
  • Huacan He
  • Yingcang Ma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4114)

Abstract

Fourteen properties and their interdependencies contributed to the analysis of six classes implication operators–S-implications, R-implications, QL-implications, Force implication, f- generated implication operator and g- generated implication operator– are explored in this paper. It is found that all the properties can be inferred from three mutually independent properties. Then, the proven concerning which properties are true, false or satisfied for each of the six classes of implication operators is given. Based on which, the author get the property I(x(n(x)) = n (x) for all x ∈[0,1] that does not hold for force implication, f-generated implication operator and g-generated implication operator.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jiaxin Han
    • 1
  • Huacan He
    • 1
  • Yingcang Ma
    • 2
  1. 1.School of Computer Science, Northwestern Polytechnical University, Xi’anChina
  2. 2.College of Science, Xi’an University of Engineering Science and Technology, Xi’anChina

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