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On the Intuitionistic Fuzzy Implications and Negations. Part 1

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35 Years of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 261))

Abstract

The paper contains review and new results related to the first 23 of the 138 already introduced by the author different intuitionistic fuzzy implications and the first 5 of the 36 different intuitionistic fuzzy negations. Some of their basic properties are studied. The validity and non-validity of the Law of Excluded Middle and its modifications, and of De Morgan’s Laws and their modifications are discussed. The axioms of Intuitionistic Logic are checked for the intuitionistic fuzzy implications and negations.

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Author information

Authors and Affiliations

  1. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia, 1113, Bulgaria

    Krassimir T. Atanassov

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  1. Krassimir T. Atanassov
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Editors and Affiliations

  1. Ghent University, Gent, Belgium

    Chris Cornelis , Glad Deschrijver , Mike Nachtegael , Steven Schockaert  & Yun Shi , , ,  & 

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Atanassov, K.T. (2010). On the Intuitionistic Fuzzy Implications and Negations. Part 1. In: Cornelis, C., Deschrijver, G., Nachtegael, M., Schockaert, S., Shi, Y. (eds) 35 Years of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16629-7_2

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  • DOI: https://doi.org/10.1007/978-3-642-16629-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16628-0

  • Online ISBN: 978-3-642-16629-7

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