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M-bornologies on L-valued Sets

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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 643))

Abstract

We develop an approach to the concept of bornology in the framework of many-valued mathematical structures. It is based on the introduced concept of an M-bornology on an L-valued set (X, E), or an LM-bornology for short; here L is an iccl-monoid, M is a completely distributive lattice and \(E: X\times X \rightarrow L\) is an L-valued equality on the set X. We develop the basics of the theory of LM-bornological spaces and initiate the study of the category of LM-bornological spaces and appropriately defined bounded “mappings” of such spaces.

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Notes

  1. 1.

    The concepts called here an L-relation and L-valued equality under different names and with different degrees of generality appear in many papers, see e.g. [26, 27], etc.

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Acknowledgement

The authors are grateful to an anonymous referee for pointing out some misprints and other minor defects noticed in the first version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Latvia, Zellu street 25, Riga, 1002, Latvia

    Ingrīda Uļjane & Alexander Šostak

  2. Institute of Mathematics and CS UL, Raina bulv. 29, Riga, 1459, Latvia

    Ingrīda Uļjane & Alexander Šostak

Authors
  1. Ingrīda Uļjane
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  2. Alexander Šostak
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Corresponding author

Correspondence to Ingrīda Uļjane .

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

    Slawomir Zadrożny

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

    Krassimir T. Atanassov

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

    Maciej Krawczak

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Uļjane, I., Šostak, A. (2018). M-bornologies on L-valued Sets. 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 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_41

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  • DOI: https://doi.org/10.1007/978-3-319-66827-7_41

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  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

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