Topological properties of fuzzy numbers

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Abstract

Fuzzy numbers are defined and a metric is assigned to this class of fuzzy sets. Topological properties of the resulting metric space are studied. The notion of θ-crisp fuzzy numbers is introduced, and, in particular, it is shown that this class of fuzzy numbers is homeomorphic to the Hilbert cube. © 1983 North-Holland.

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Goetschel, R., & Voxman, W. (1983). Topological properties of fuzzy numbers. Fuzzy Sets and Systems, 10(1–3), 87–99. https://doi.org/10.1016/S0165-0114(83)80107-9

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