Abstract
For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ℓ2 if Y is compact; and the space F(Rn) is also homeomorphic to ℓ2.
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