A note on intuitionistic fuzzy metric spaces. (English) Zbl 1096.54003
Summary: Recently, J. H. Park [Chaos Solitons Fractals 22, 1039–1046 (2004; Zbl 1060.54010)] introduced and studied a notion of intuitionistic fuzzy metric space by using the idea of intuitionistic fuzzy set due to Atanassov. In this note we show that for each intuitionistic fuzzy metric space \((X, M, N, *, \diamondsuit)\), the topology generated by the intuitionistic fuzzy metric\( (M, N)\) coincides with the topology generated by the fuzzy metric \(M\), and hence, the study of the space \((X, M, N, *, \diamondsuit)\) reduces to the study of the fuzzy metric space \((X, M, *)\), such that, Park’s results follow directly from well-known theorems in fuzzy metric spaces.
MSC:
| 54A40 | Fuzzy topology |
Citations:
Zbl 1060.54010References:
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