Lipschitz functions and fuzzy number approximations

We prove that some important properties of convex subsets of vector topological spaces remain valid in the space of fuzzy numbers endowed with the Euclidean distance. We use these results to obtain a characterization of fuzzy number-valued Lipschitz functions. This fact helps us to find the best Lipschitz constant of the trapezoidal approximation operator preserving the value and ambiguity introduced in a recent paper. Finally, applications in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the value and ambiguity in the case when the direct formula is not applicable and an estimation for the defect of additivity of the trapezoidal approximation preserving the value and ambiguity are given.