The topological structure of fuzzy sets with sendograph metric |
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Authors: | Lili Zhang |
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Institution: | Department of Mathematics, Xi?an Technological University, Xi?an, Shaanxi, 710032, PR China |
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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 ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. |
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Keywords: | 54B20 03E72 57N20 |
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