Generalizing a Construction of Non-Strong Fuzzy Metrics from Metrics and Studying Their Induced Topology

The problem of obtaining new examples of fuzzy metrics is of interest, as this type of fuzzy measurement has been proven to be useful in engineering applications. In this context, different works have addressed the problem of deriving fuzzy metrics from classical ones. This paper is devoted to generalizing a construction of non-strong fuzzy metrics from metrics already provided in the literature, both for continuous Archimedean t-norms and for the minimum t-norm. Moreover, we explore the conditions under which one adapts this generalized method to obtain fuzzy metrics in the sense of George and Veeramani. In addition, we investigate the connection between the topology associated with the fuzzy metric constructed via these procedures and that determined by the metric. Several examples are provided to support and illustrate our findings.