Finite dimensional fuzzy normed linear space
Fuzzy Sets and Systems
On some results in fuzzy metric spaces
Fuzzy Sets and Systems
On some results of analysis for fuzzy metric spaces
Fuzzy Sets and Systems
The completions of fuzzy metric spaces and fuzzy normed linear spaces
Fuzzy Sets and Systems
On completion of fuzzy metric spaces
Fuzzy Sets and Systems - Fuzzy intervals
A note on the completions of fuzzy metric spaces and fuzzy normed spaces
Fuzzy Sets and Systems - Mathematics
On the triangle inequalities in fuzzy metric spaces
Information Sciences: an International Journal
An improved completion theorem of fuzzy metric spaces
Fuzzy Sets and Systems
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This paper discusses the completion of a fuzzy metric space (in the sense of Kaleva and Seikkala) that is modeled by a pair of two-place functions, L and R. Previous work on this question is based on L=min, R=max. Under the condition that L and R are a generic class of two-place functions, we characterize the completable fuzzy metric space and show that the corresponding completion is uniquely determined up to isometry. Furthermore, we point out that with more conditions on R, including on R=max, the completion of each fuzzy metric space exists and is unique up to isometry. This improves the corresponding result of Kaleva [The completion of fuzzy metric spaces, J. Math. Anal. Appl. 109 (1985) 194-198].