Bicompletable Standard Fuzzy Quasi-Metric Space

In [1] Kider started the study of a notion of standard fuzzy metric space that constitutes an interesting modification of the notion of metric fuzziness due to George and Veeramani [2]. In this paper we extend the notion standard fuzzy metric space to a standard fuzzy quasi-metric space [3]. On the other hand, it was presented in [4] an example of a standard fuzzy metric space that is not completable, also it has been obtained an internal characterization of completable standard fuzzy metric spaces. taking these results into account and the fact that the concept of bicompletion provides a theory of completion to quasimetric spaces in the classical sense [5]. It seems natural and interesting to discuss the problem of characterizing standard fuzzy quasi-metric spaces that are bicompletable. The main purpose of this paper is to solve this problem. Following the modern terminology of [5] by a quasi-metric on a set X we mean a function d : XX [0, ) → ∞ such that for all x, y, z ∈ X.