The Completion of a Fuzzy Normed Linear Space

The concept of a fuzzy normed linear space was introduced in an earlier paper by the author (Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems48 (1992), 239-248). It was shown therein that any finite dimensional fuzzy normed linear space is necessarily complete. There do exist incomplete fuzzy normed linear spaces. Incompleteness is shown to have handicaps (see Section 3). There is a need for completion in the sense of enlarging the incomplete space so that the given space is embedded in the enlarged space. It is shown in this paper (see Theorem 3) that this is really possible.