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

  • Alexander ŠostakEmail author
  • Raivis BētsEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (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.

Keywords

Fuzzy pseudometric Fuzzy \(\varphi \)-pseudometric Supratopology Cauchy sequences Baire category theorem 

Notes

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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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LatviaRigaLatvia
  2. 2.Institute of Mathematics and Computer ScienceULRigaLatvia

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