Abstract
As a natural generalization of fuzzy numbers, fuzzy star-shaped numbers play a crucial role in fuzzy mathematics. Let Y be a non-degenerate compact convex subset of the n-dimensional Euclidean space, and let FSz0(Y) be the family consisting of all fuzzy star-shaped numbers with respect to z0 whose supports contained in Y. Using methods from infinite-dimensional topology, we mainly show that the space FSz0(Y) with the topology induced by the sendograph metric is homeomorphic to the separable Hilbert space ℓ2.
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