Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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FUZZY METRIC SPACES

  • Xia, Zun-Quan (Laboratory 2, CORA, Department of Applied Mathematics, Dalian University of Technology) ;
  • Guo, Fang-Fang (Laboratory 2, CORA, Department of Applied Mathematics, Dalian University of Technology)
  • Published : 2004.09.01

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Abstract

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.

Keywords