Completeness of fuzzy normed linear space of all weakly fuzzy bounded linear operators

In this note, it is proved that the fuzzy normed linear space B(X,Y)B(X,Y) of all weakly fuzzy bounded linear operators defined from a Felbin's type fuzzy normed linear space X to a Felbin's type fuzzy normed space Y is complete when Y is complete, and that Y   is complete when B(X,Y)B(X,Y) is complete with some mild conditions on X.