Based on the concept of pseudocomplement, we introduce a new representation of preopenness of
L
-fuzzy sets in
R
L
-fuzzy bitopological spaces. The concepts of pairwise
R
L
-fuzzy precontinuous and pairwise
R
L
-fuzzy preirresolute functions are extended and discussed based on the
i
,
j
-
R
L
-preopen gradation. Further, we follow up with a study of pairwise
R
L
-fuzzy precompactness in
R
L
-fuzzy bitopological spaces of an
L
-fuzzy set. We find that our paper offers more general results since
R
L
-fuzzy bitopology is a generalization of
L
-bitopology,
R
L
-bitopology, and
L
-fuzzy topology.