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Characterization of compact subsets of fuzzy sets

Diamond, P. and Kloeden, P. (1989) Characterization of compact subsets of fuzzy sets. Fuzzy Sets and Systems, 29 (3). pp. 341-348.

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A characterization of compact subsets is presented for the metric space of normal fuzzy convex fuzzy sets on the base space Rn, the metric for which is the supremum over the Hausdorff distances between corresponding level sets. It is shown that a closed subset is compact if and only if it is uniformly support-bounded and the corresponding set of support functions is equileftcontinuous in the membership grade variable.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Elsevier B.V.
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