Fuzzy bicompletable quasi-fuzzy distance space

In this paper we introduce the definition of quasi-fuzzy distance space then we discuss several properties of this space after we give an example to illustrate this notion. Then we show that the existence of a quasi-fuzzy distance space which is not fuzzy bicompletable. Here we prove that every fuzzy bicompletable quasi-fuzzy distance space admits a unique [up to fuzzy isodistance] fuzzy a bicompletion.