A duality relationship between fuzzy metrics and metrics. Issue 6 (18th August 2018) - Miñana, Juan-José; Valero, Oscar
ABSTRACT: Based on the duality relationship between indistinguishability operators and (pseudo-)metrics, we address the problem of establishing whether there is a relationship between the last ones and fuzzy (pseudo-)metrics. We give a positive answer to the posed question. Concretely, we yield a method for generating fuzzy (pseudo-)metrics from (pseudo)-metrics and vice versa. The aforementioned methods involve the use of the pseudo-inverse of the additive generator of a continuous Archimedean t -norm. As a consequence, we get a method to generate non-strong fuzzy (pseudo-)metrics from (pseudo-)metrics. Examples that illustrate the exposed methods are also given. Finally, we show that the classical duality relationship between indistinguishability operators and (pseudo)-metrics can be retrieved as a particular case of our results when continuous Archimedean t -norms are under consideration.