A new characterization of compact sets in fuzzy number spaces. (English) Zbl 1439.54006

Huang, Huan; Wu, Congxin

Abstr. Appl. Anal. 2013, Article ID 820141, 6 p. (2013).

Summary: We give a new characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that some previous compactness criteria are wrong. A counterexample also is given to validate this judgment.

MSC:

54A40	Fuzzy topology
54D30	Compactness

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