模糊度量空间的完备性特征

Characterization of Completcrice for Fuzzy Metric Space

在Kaleva和Seikkala引入的模糊度量空间框架下,研究它的完备性特征。引入了模糊度量空间中子集的模糊有界性和模糊直径的概念,在此基础上证明了模糊度量空间的一个充分必要条件,它类似于表征通常度量空间完备性的G.Cantor定理。

Under the definition of fuzzy metric space introduce by kaleva and Seikkala, We define the concepts: bounded fuzzy subset, diameter of a fuzzy subset. Then we prove a theorem which characterize the completencess of fuzzy metric space. This theorem is a fuzzy generalization of G. Cantor's theorem for metric spaces.