An embedding theorem for fuzzy numbers on Banach spaces and its applications
In this work, we give an embedding theorem for fuzzy number space 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 Butnariu (Fuzzy Sets and Systems 31 (1989) 77). Additionally, we generalize some convergence theorems and Lusin Theorem to fuzzy random variables. (C) 2002 Elsevier Science B.V. All rights reserved.
embedding theorem fuzzy numbers convergence theorems lusin theorem fuzzy random variables analysis