A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps

Abstract

In the paper [E. Jiménez-Fernández, J. Rodríguez-López, E. A. Sánchez Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so called Euclidean fuzzy metric space (R, Mϕ,g, ∗). However, while the function ϕ is only required to be increasing, some results of the paper implicitly assume that ϕ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires ϕ to be also left-continuous.