Relationships between completeness of fuzzy quasi-uniform spaces

In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-lters. Utilizing the relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities, we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationships between the completeness of induced probabilistic quasi-uniform spaces and both completeness of induced classical quasi-uniform spaces and induced Hutton [0, 1]-quasi-uniform spaces.