An embedding theorem for fuzzy numbers on Banach spaces and its applications (Q698803)

Sumamry: We give an embedding theorem for fuzzy number space \(\mathbb{N}(X)\) on a Banach space \(X\). As its applications, we show that some measurability concepts for fuzzy number valued mappings are equivalent, which partially solves an open problem given by \textit{D. Butnariu} [Fuzzy Sets Syst. 31, 77-82 (1989; Zbl 0664.28011)]. Additionally, we generalize some convergence theorems and Lusin Theorem to fuzzy random variables.