An identification theorem for the completion of the Hausdorff fuzzy metric

We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff fuzzy metrics are defined on the respective collections of non-empty closed subsets. As a consequence, we deduce the corresponding result for metric spaces by using the standard fuzzy metric. An application to the extension of multivalued mappings and some illustrative examples are also given.Research supported by the Ministry of Economy and Competitiveness of Spain, under Grants MTM2012-37894-C02-01 and MTM2012-37894-C02-02. The first named author also acknowledges financial support from the UPV/EHU under Grants UFI 11/52 and GIU12/39.Gutierrez García, J.; Romaguera Bonilla, S.; Sanchis, M. (2013). An identification theorem for the completion of the Hausdorff fuzzy metric. Fuzzy Sets and Systems. 227:96-106. https://doi.org/10.1016/j.fss.2013.04.0129610622