In this paper we introduce the definition of standard fuzzy normed space then we discuss several properties after we give an example to illustrate this notion. After that we showed the existence of a standard fuzzy normed space which is not completable. Here we prove that every completable standard fuzzy normed space admits a unique [up to F-isometric] completation.
Key Words: Standard fuzzy normed space, F-bounded set, completable standard fuzzy normed space
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