Fuster-Parra, PilarMartin, JavierRecasens, JordiValero, Oscar2024-09-132024-09-132020-04Fuster-Parra P, Martin J, Recasens J, Valero O. T-Equivalences: The Metric Behavior Revisited. Mathematics. 2020 Apr;8(4):495.http://hdl.handle.net/20.500.13003/11143https://hdl.handle.net/20.500.12105/22954Since the notion of T-equivalence, where T is a t-norm, was introduced as a fuzzy generalization of the notion of crisp equivalence relation, many researchers have worked in the study of the metric behavior of such fuzzy relations. Concretely, a few techniques to induce metrics from T-equivalences, and vice versa, have been developed. In several fields of computer science and artificial intelligence, a generalization of pseudo-metric, known as partial pseudo-metrics, have shown to be useful. Recently, Bukatin, Kopperman and Matthews have stated that the notion of partial pseudo-metric and a type of generalized T-equivalence are linked. Inspired by the preceding fact, in this paper, we state a concrete relationship between partial pseudo-metrics and the aforesaid generalized T-equivalences. Specifically, a method for constructing partial pseudo-metrics from the new type of T-equivalences and, reciprocally, for constructing the generalized T-equivalences from partial pseudo-metrics are provided. However, important differences between the new approach and the classical one are established. Special interest is paid to the case in which the minimum, drastic, and ukasiewicz t-norms are under consideration.enghttp://creativecommons.org/licenses/by/4.0/Continuous t-normArchimedean t-normAdditive generatorT-equivalenceT-equalityPartial pseudo-metricresearch articleAttribution 4.0 International8449510.3390/math80404952227-7390Mathematicsopen access2-s2.0-85084517774531824100035