This paper first reviewed the two main versions of fuzzy metrics,and pointed out their differences in their definitions.Then,it introduced a concept of basic fuzzy metric space containing most of the existing fuzzy metrics and gave its decomposition theorem.On this basis,the author investigated the relationships between some special axioms of fuzzy metric and the decomposition theorems for various fuzzy metric spaces and conducted a comparative study of different fuzzy metrics from the perspective of decomposition theorem.The results obtained are of great significance to further understand the characteristics of different fuzzy metrics,and reveal the internal relationship between a fuzzy metric and a crisp metric(families).They provide a new way for the further study of fuzzy metric theory.
维普
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