A duality relationship between fuzzy metrics and metrics |
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Authors: | Juan-José Miñana Oscar Valero |
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Affiliation: | Departamento de Ciencias Matemáticas e Informática, Universidad de las Islas Baleares, Palma, Spain |
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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. |
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Keywords: | Fuzzy (pseudo-)metric indistinguishability operator continuous Archimedean t-norm additive generator pseudo-inverse (pseudo-)metric |
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