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A Note on Extension of Fuzzy Metric Spaces

Author

Listed:
  • Dingwei Zheng

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Qingming He

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

Abstract

In this note, we prove that for two compatible fuzzy metrics M H and M K on H and K , respectively, there exists a fuzzy metric M on H ⋃ K such that M | H = M H and M | K = M K under the conditions that t-norm ∗ is positive and fuzzy metrics M H , M K are strong, or t-norm ∗ is positive and t-norm ∗, fuzzy metrics M H , M K satisfy the Lipschitz conditions.

Suggested Citation

  • Dingwei Zheng & Qingming He, 2023. "A Note on Extension of Fuzzy Metric Spaces," Mathematics, MDPI, vol. 11(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4898-:d:1296100
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