Fuzzy metric spaces

Journal of Applied Mathematics and Computing 01/2004; 16(1):371-381. DOI: 10.1007/BF02936175


In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of
fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a
fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy
metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research
on fuzzy optimization and pattern recognition.

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Available from: Fang-Fang Guo, Oct 29, 2014