Preopenness Degree in RL-Fuzzy Bitopological Spaces

Abstract

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.