Convergence of fuzzy sets with respect to the supremum metric

Abstract

ElsevierPedraza 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. doi:10.1016/j.fss.2014.03.005. CONVERGENCE OF FUZZY SETS WITH RESPECT TO THE SUPREMUM METRICTATIANA PEDRAZA, JESÚS RODRÍGUEZ-LÓPEZ ⋆, * AND SALVADOR ROMAGUERA * Abstract. We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric 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 behaviour of the convergence in the supremum metric with respect to maximizers.