Gromov-Hausdorff convergence of non-Archimedean fuzzy metric spaces. (English) Zbl 1392.54012
Summary: We introduce the notion of the Gromov-Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of I. Kramosil and J. Michalek [Kybernetika 11, 336–344 (1975; Zbl 0319.54002)]). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov-Hausdorff distance on metric spaces can be deduced from our approach.
MSC:
| 54A40 | Fuzzy topology |
| 54E35 | Metric spaces, metrizability |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
Citations:
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