A note on the completions of fuzzy metric spaces and fuzzy normed spaces. (English) Zbl 1012.54006
Summary: In this paper, we point out that the completion theorem of fuzzy metric spaces given by B. S. Lee, S. J. Lee and K. M. Pack [Fuzzy Sets Syst. 106, No. 3, 496-473 (1999; Zbl 0987.54015)] is incorrect and prove a new completion theorem.
MSC:
| 54A40 | Fuzzy topology |
| 54D35 | Extensions of spaces (compactifications, supercompactifications, completions, etc.) |
| 46S40 | Fuzzy functional analysis |
| 54E35 | Metric spaces, metrizability |
| 54E50 | Complete metric spaces |
Citations:
Zbl 0987.54015References:
| [1] | Diamond, P.; Kloeden, P., Metric Spaces of Fuzzy Sets, Theory and Applications (1994), World Scientific: World Scientific Singapore · Zbl 0873.54019 |
| [2] | Felbin, C., Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48, 239-248 (1992) · Zbl 0770.46038 |
| [3] | Kaleva, O.; Seikkala, S., On fuzzy metric spaces, Fuzzy Sets and Systems, 12, 215-229 (1984) · Zbl 0558.54003 |
| [4] | Lee, B. S.; Lee, S. J.; Park, K. M., The completions of fuzzy metric spaces and fuzzy normed spaces, Fuzzy Sets and Systems, 106, 469-473 (1999) · Zbl 0987.54015 |
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