Elsevier

Fuzzy Sets and Systems

Volume 159, Issue 16, 16 August 2008, Pages 2104-2115
Fuzzy Sets and Systems

Some notes on the characterization of compact sets of fuzzy sets with Lp metric

https://doi.org/10.1016/j.fss.2007.11.010Get rights and content

Abstract

In 1990, Diamond gave a characterization of compact sets in the space of fuzzy star-shaped numbers with respect to the origin with Lp metric for 1p<. Later on, Ming modified the characterization of compact sets in the space of fuzzy numbers with Lp metric for 1p<. In this paper, we point out that the characterization of Diamond and the modified one of Ma Ming are incorrect by two counterexamples, and we get correct characterizations for compact sets in spaces of fuzzy star-shaped numbers with respect to the origin and fuzzy numbers with Lp metric for 1p<, correspondingly.

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This work is supported by the NSFC (No. 10571035).

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