Abstract
Recently, V. Gregori, S. Morillas and A. Sapena have discussed [On a class of completable fuzzy metric spaces, Fuzzy Sets and Systems 161 (2010), 2193-2205] the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of A. George and P. Veeramani and state the question of finding a non-strong fuzzy metric space for a continuous t-norm different from the minimum. Later on, J. Gutiérrez García and S. Romaguera solved this question [Examples of non-strong fuzzy metrics, Fuzzy Sets and Systems 162 (2011) 91-93] by means of two examples for the product and the Lukasiewicz t-norm, respectively. In this direction they posed to find further examples of non-strong fuzzy metrics for continuous t-norm that are greater than the product but different from minimum. In this paper we obtain, among others facts on t-norms and fuzzy metric spaces, an example of this kind.
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