On Yager and Hamacher t-Norms and Fuzzy Metric Spaces

Recently, Gregori etal. have discussed (Fuzzy Sets Syst 2011;161:2193-2205) the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of George and Veeramani and state the question of finding a nonstrong fuzzy metric space for a continuous t-norm different from the minimum. Later on, Gutierrez Garcia and Romaguera solved this question (Fuzzy Sets Syst 2011;162:91-93) by means of two examples for the product and the Lukasiewicz t-norm, respectively. In this direction, they posed to find further examples of nonstrong fuzzy metrics for continuous t-norms that are greater than the product but different from minimum. In this paper, we found an example of this kind. On the other hand, Tirado established (Fixed Point Theory 2012;13:273-283) a fixed-point theorem in fuzzy metric spaces, which was successfully used to prove the existence and uniqueness of solution for the recurrence equation associated with the probabilistic divide and conquer algorithms. Here, we generalize this result by using a class of continuous t-norms known as -Yager t-norms.