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Intuitionistic Fuzzy Tautology Definitions for the Validity of Intuitionistic Fuzzy Implications: An Experimental Study

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Intelligent Systems'2014

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 322))

Abstract

The central issue of inference validity, that guarantees the correctness of reasoning and thus that of derived knowledge, depends on the definition of both implication operator and tautology. This paper studies the modus ponens validity in the case of Intuitionistic Fuzzy logic, in an experimental framework: considering 18 classical implication operators, it shows that validity usually does not hold for the classical definition of Intuitionistic Fuzzy tautology. It proposes two alternative, more constrained, tautology definitions, studying them with the same protocol, showing they make it possible to decrease the number of invalid implication operators.

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References

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Author information

Authors and Affiliations

  1. CNRS, UMR 7606, LIP6, Paris, France

    Marcin Detyniecki, Marie-Jeanne Lesot & Paul Moncuquet

  2. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, Paris, France

    Marcin Detyniecki, Marie-Jeanne Lesot & Paul Moncuquet

  3. Polish Academy of Sciences, IBS PAN, Warsaw, Poland

    Marcin Detyniecki

Authors
  1. Marcin Detyniecki
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  2. Marie-Jeanne Lesot
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  3. Paul Moncuquet
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Editor information

Editors and Affiliations

  1. School of Computing and Communications, Lancaster University, Lancaster, United Kingdom

    P. Angelov

  2. Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K.T. Atanassov

  3. Intelligent Systems Department, Bulgarian Academy of Sciences Inst. of Infor. & Communication Techn., Sofia, Bulgaria

    L. Doukovska

  4. Metalurgy, University of Chemical Technology and, Sofia, Bulgaria

    M. Hadjiski

  5. University of Library Studies and IT (ULSIT), Sofia, Bulgaria

    V. Jotsov

  6. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    J. Kacprzyk

  7. Knowledge Engineering and Discovery Research Institute, Auckland University of Technology, Auckland, New Zealand

    N. Kasabov

  8. Intelligent Systems Laboratory, Prof. Assen Zlatarov University Faculty of Technical Sciences, Bourgas, Bulgaria

    S. Sotirov

  9. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    E. Szmidt

  10. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    S. Zadrożny

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Detyniecki, M., Lesot, MJ., Moncuquet, P. (2015). Intuitionistic Fuzzy Tautology Definitions for the Validity of Intuitionistic Fuzzy Implications: An Experimental Study. In: Angelov, P., et al. Intelligent Systems'2014. Advances in Intelligent Systems and Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-11313-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-11313-5_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11312-8

  • Online ISBN: 978-3-319-11313-5

  • eBook Packages: EngineeringEngineering (R0)

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