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Fuzzy \(\varphi \)-pseudometrics and Fuzzy \(\varphi \)-pseudometric Spaces

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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

By replacing the axiom \(m(x,x,t) = 1\) for all \(x\in X, t>0\) in the definition of a fuzzy pseudometric in the sense of George-Veeramani with a weaker axiom \(m(x,x,t) = \varphi (t)\) for all \(x\in X, t>0\) where \(\varphi : {\mathbb R}^+ \rightarrow (0,1]\) is a non-decreasing function, we come to the concept of a fuzzy \(\varphi \)-pseudometric space. Basic properties of fuzzy \(\varphi \)-pseudometric spaces and their mappings are studied. We show also an application of fuzzy \(\varphi \)-pseudometrics in the words combinatorics.

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Acknowledgment

The authors are grateful to the anonymous referees 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, Riga, 1002, Latvia

    Alexander Šostak & Raivis Bēts

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

    Alexander Šostak

Authors
  1. Alexander Šostak
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  2. Raivis Bēts
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Corresponding authors

Correspondence to Alexander Šostak or Raivis Bēts .

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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Šostak, A., Bēts, R. (2018). Fuzzy \(\varphi \)-pseudometrics and Fuzzy \(\varphi \)-pseudometric Spaces. 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_30

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  • DOI: https://doi.org/10.1007/978-3-319-66827-7_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

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