Abstract
In this paper, we introduce a formula to induce metrics from a fuzzy ultrametric, and consider consistency of the metrics. We also show that completeness and precompactness of a fuzzy ultrametric space are, respectively, identical with completeness and totally bounded property of the metric spaces induced by the fuzzy ultrametric. Furthermore, we explore three types of Hausdorff fuzzy metrics in a fuzzy metric space, and prove that they are identical if the fuzzy metric space is a fuzzy ultrametric space. At last, we discuss consistency between the Hausdorff fuzzy metric in a fuzzy ultrametric space and the Hausdorff metric in the metric space induced by this fuzzy ultrametric.
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