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October 1, 2025AxiomsOpen Access

A Type of Fuzzy Metric and Its Applications

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The research presents a construction theorem for lattice-valued fuzzy metrics, focusing on L-quasi metrics.
An equivalent characterization is provided through C-nbd clusters, which form basic spheres critical to the study.
Relationships among the four types of basic spheres are examined, revealing key topological properties of metrics.
A new fuzzy p-metric is introduced, demonstrating that the L-real line satisfies its characteristics within this framework.

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This paper investigates fuzzy metrics in L-topology, showing how C-nbd clusters characterize these metrics.

鹏陈 (2025) studied this question.

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