Embedding problem of noncompact fuzzy number space En

It is well known that functional analysis is a very useful tool in many branches of mathematics science. M L. Puri and D.A. Ralescu (1983) made use of H. Radstrom´s (1952) embedding theorem, isometrically embedding the n-dimensional fuzzy number space Eⁿ into some Banach space. Following this embedding theorem, M.L. Puri and D.A. Ralescu (1986) and O. Kaleva (1987; 1990) discussed the measurability, integrability and differentiability of fuzzy number-valued mappings. The article investigates the weak measurability, weak integrability and weak differentiability of fuzzy number-valued mappings by means of the corresponding knowledge of abstract functions in functional analysis (Wu Congxin and Ma Ming, 1992)