2026-04-29T12:23:04Zhttps://repisalud.isciii.es/rest/oai/requestoai:repisalud.isciii.es:20.500.12105/229862024-11-29T07:47:32Zcom_20.500.12105_15322com_20.500.12105_2051col_20.500.12105_16967
Repisalud
author
Gregori, Valentin
author
Minana, Juan-Jose
author
Miravet, David
2024-09-13T09:14:50Z
2024-09-13T09:14:50Z
2020-09
Gregori V, Minana JJ, Miravet D. A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics. Mathematics. 2020 Sep;8(9):1575.
10.3390/math8091575
2227-7390
Mathematics
https://hdl.handle.net/20.500.13003/19406
2-s2.0-85091496239
https://hdl.handle.net/20.500.12105/22986
581486500001
In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm *. Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm * is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship.
eng
Fuzzy quasi-metric
Fuzzy partial metric
Additive generator
Residuum operator
Archimedean t-norm
A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics
research article