Convergence of fuzzy sets with respect to the supremum metric

Abstract

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the alpha-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasi-pseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also provide some results about the behavior of the convergence in the supremum metric with respect to maximizers. (C) 2014 Elsevier B.V. All rights reserved.The second and third authors thank the support of the Ministry of Economy and Competitiveness of Spain under grant MTM2012-37894-C02-01.Pedraza Aguilera, T.; Rodríguez López, J.; Romaguera Bonilla, S. (2014). Convergence of fuzzy sets with respect to the supremum metric. Fuzzy Sets and Systems. 245:83-100. https://doi.org/10.1016/j.fss.2014.03.005S8310024