Gromov–Hausdorff convergence of non-Archimedean fuzzy metric spaces

Abstract

We introduce the notion of the Gromov–Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). 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.