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A Survey on Nullnorms 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

Nullnorms are generalizations of triangular norms (t-norms) and triangular conorms (t-conorms) with a zero element to be an arbitrary point from an arbitrary bounded lattice. In this paper, we study nullnorms on bounded lattices. We examine some properties of nullnorms considering the concepts of idempotency, local internality, conjunctivity and disjunctivity on bounded lattices. We investigate relationships between such concepts for nullnorms on bounded lattices and some illustrative examples are added to clearly show connections between these. Moreover, we give two methods to obtain nullnorms on bounded lattices with a zero element by using the given nullnorm and t-norm (t-conorm) with some constraints.

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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 & Funda Karaçal

Authors
  1. Gül Deniz Çaylı
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  2. Funda Karaçal
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Corresponding author

Correspondence to Gül Deniz Çaylı .

Editor information

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., Karaçal, F. (2018). A Survey on Nullnorms 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_39

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_39

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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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