Preopenness Degree in R L -Fuzzy Bitopological Spaces

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