On the integrable noncompact fuzzy number space (Q847383)

The concept of integrable noncompact fuzzy number is proposed. Representation theorems showing the representability of integrable noncompact fuzzy numbers by intervals and functions are also presented. The integrable noncompact fuzzy numbers form an integrable noncompact fuzzy number space \(\hat E\) that has the existing fuzzy number space \(E^{1}\) as a subspace. With a metric \(d^{1}, (\hat E,d^1)\) is proven to be complete and separable and it is the completed space of \(E^{1}\) with respect to the metric \(d^{1}\). It is also proven that \(\hat E\) can be embedded into a concrete Banach space \(L(0,1]\times L(0,1]\) isometrically and isomorphically.