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Characterizing Ordinal Sum for t-norms and t-conorms on Bounded Lattices

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 641))

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Abstract

The ordinal sum of triangular norms on the unit interval has been proposed to construct new triangular norms. However, considering general bounded lattices, the ordinal sum of triangular norms and conorms may not generate triangular norms and conorms. In this paper, we study and propose some new construction methods yielding triangular norms and conorms on general bounded lattices. Moreover, we generalize these construction methods by induction to a ordinal sum construction for triangular norms and conorms, applicable on any bounded lattice. And some illustrative examples are added for clarity.

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Acknowledgments

The authors are very grateful to the anonymous reviewers and editors for their helpful comments and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080, Trabzon, Turkey

    Gül Deniz Çaylı

Authors
  1. Gül Deniz Çaylı
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Correspondence to Gül Deniz Çaylı .

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Editors and Affiliations

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

    Janusz Kacprzyk

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

    Eulalia Szmidt

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

    Sławomir Zadrożny

  4. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Çaylı, G.D. (2018). Characterizing Ordinal Sum for t-norms and t-conorms on Bounded Lattices. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_40

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66829-1

  • Online ISBN: 978-3-319-66830-7

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