证明论域X上的全体模糊集之集上的两种度量是等价的。讨论这种度量空间中孤立点的分布情况, 并将这些结论推广到格值模糊集之集上。从模糊推理系统鲁棒性分析的角度, 比较几种不同的蕴涵算子生成的度量或者拓扑。

The equivalence of two metrics on the family of fuzzy subsets of the universe X is verified. The distributions of isolated points of the above metric spaces are discussed, and these investigations were extended to the set that consist of lattice-valued fuzzy subsets. Different metrics or topologies which generated by different implication operators are compared from the view point of robustness analysis of fuzzy reasoning system.