Kybernetika 49 no. 1, 141-148, 2013

The strongest t-norm for fuzzy metric spaces

Dong Qiu and Weiquan Zhang

Abstract:

In this paper, we prove that for a given positive continuous t-norm there is a fuzzy metric space in the sense of George and Veeramani, for which the given t-norm is the strongest one. For the opposite problem, we obtain that there is a fuzzy metric space for which there is no strongest t-norm. As an application of the main results, it is shown that there are infinite non-isometric fuzzy metrics on an infinite set.

Keywords:

fuzzy metric space, t-norm, isometry, analysis

Classification:

93E12, 62A10

paper.pdf

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