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

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 1⩽p<∞. Later on, Ming modified the characterization of compact sets in the space of fuzzy numbers with Lp metric for 1⩽p<∞. 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 1⩽p<∞, correspondingly.