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00925njm 22002777a 4500 dc Miñana, Juan-José author Šostak, Alexander author Valero, Oscar author 2023 It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy metric, whenever it is defined by means of an Archimedean t-norm, has recently been introduced in the literature. Motivated by this fact, we focus our efforts on such a method in this paper. We prove that the topology induced by a given fuzzy metric M and the topology induced by the metric constructed from M by means of such a method coincide. Besides, we prove that the completeness of the fuzzy metric space is equivalent to the completeness of the associated classical metric obtained by the aforementioned method. Moreover, such results are applied to obtain fuzzy versions of two well-known classical fixed point theorems in metric spaces, one due to Matkowski and the other one proved by Meir and Keeler. Although such theorems have already been adapted to the fuzzy context in the literature, we show an inconvenience on their applicability which motivates the introduction of these two new fuzzy versions. Miñana J-J, Šostak A, Valero O. On metrization of fuzzy metrics and application to fixed point theory. Fuzzy Sets Syst. 2023 Sep;468:108625. 10.1016/j.fss.2023.108625 0165-0114 Fuzzy Sets and Systems https://hdl.handle.net/20.500.13003/19340 https://hdl.handle.net/20.500.12105/23732 1027652100001 On metrization of fuzzy metrics and application to fixed point theory