The concept of n-cut cube fuzzy numbers and embedding theorem

In this paper, we introduce the concept of n - cut cube fuzzy numbers, discuss their operations and representation theorems, define a complete metric DL on the n -cut cube fuzzy number space L(Eⁿ) and prove DL⩽ D⩽√nDL, and obtain a embedding theorem of (L(Eⁿ),DL) (isometrically embeds (L(E ⁿ), DL) into a concrete Banach space Π_r=1 ²ⁿ C_i[O,l]). We also consider the differential of n - cut fuzzy number value mapping F : [a, b] → L(Eⁿ) by using the embedding theorem, where a, b E R