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00925njm 22002777a 4500 dc Gregori, Valentin author Minana, Juan-Jose author Miravet, David author 2020-09 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. 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 Fuzzy quasi-metric Fuzzy partial metric Additive generator Residuum operator Archimedean t-norm A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics