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(E/sup n/) and prove DL/spl les/ D/spl les//spl radic/nDL, and obtain a embedding theorem of (L(E/sup n/),DL) (isometrically embeds (L(E/sup n/), DL) into a concrete Banach space /spl Pi//sub r=1/ /sup 2n/ C/sub i/[O,l]). We also consider the differential of n - cut fuzzy number value mapping F : [a, b] /spl rarr/ L(E/sup n/) by using the embedding theorem, where a, b E R.