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Uninorms on Bounded Lattices – Recent Development

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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))

Abstract

The main goal of this paper is to explore whether on every bonded lattice L, possessing incomparable elements, one can choose incomparable elements \(\mathbf {e}\) and \(\mathbf {a}\) and then to construct a uninorm on L having \(\mathbf {e}\) and \(\mathbf {a}\) as its neutral and absorbing elements, respectively. Some necessary and some sufficient conditions for construction of uninorms on L which are neither conjunctive nor disjunctive, are given. Example of an infinite bounded lattice on which only conjunctive and disjunctive uninorms exist is presented.

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Acknowledgement

The work of Martin Kalina has been supported from the Science and Technology Assistance Agency under contract No. APVV-14-0013, and from the VEGA grant agency, grant No. 2/0069/16.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University-Kingsville, MSC 172, Kingsville, TX, 78363, USA

    Slavka Bodjanova

  2. Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05, Bratislava, Slovakia

    Martin Kalina

Authors
  1. Slavka Bodjanova
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  2. Martin Kalina
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Corresponding author

Correspondence to Martin Kalina .

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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Bodjanova, S., Kalina, M. (2018). Uninorms on Bounded Lattices – Recent Development. 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_21

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_21

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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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