On the integrable noncompact fuzzy number space

In this paper an extension of the existing fuzzy number, called integrable noncompact fuzzy number, is proposed. The representation theorems of integrable noncompact fuzzy number by intervals and functions are also presented. All the integrable noncompact fuzzy numbers form an integrable noncompact fuzzy number space Eˆ that makes the existing fuzzy number space E1E1 as its subspace. With a metric d1d1, (Eˆ,d1) is proven to be complete and separable and is the completed space of E1E1 with respect to the metric d1d1. It is also proven that Eˆ can be embedded into a concrete Banach space L(0,1]×L(0,1]L(0,1]×L(0,1] isometrically and isomorphically.