Abstract
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.
Highlights
The fuzzy set theory was introduced in the year 1965 by Lotfi A
In 1991, Bin Shahna [2] introduced the concept of αopen and preopen sets in the context of fuzzy sets, and he introduced a preliminary study of fuzzy strong semicontinuity and fuzzy precontinuity as well
The concepts of fuzzy α-open sets, fuzzy preopen, fuzzy α-continuous mappings, and fuzzy precontinuous mappings have been generalized to the setting of fuzzy bitopological spaces in [3], where some of their fundamental properties have been studied
Summary
The fuzzy set theory was introduced in the year 1965 by Lotfi A. The concepts of fuzzy α-open sets, fuzzy preopen, fuzzy α-continuous mappings, and fuzzy precontinuous mappings have been generalized to the setting of fuzzy bitopological spaces in [3], where some of their fundamental properties have been studied. Shi [4] presented the concept of an L-fuzzy preopen degree of L-fuzzy set in L-fuzzy topological spaces. He discussed the fundamental properties of L-fuzzy precontinuous and L-fuzzy preirresolute mappings. It is clear that the gradation of fuzzy compactness and Lindelöf property in the sense of Kubiak and Šostak are special cases of the corresponding degrees in RL-fuzzy topology. We introduce and discuss pairwise RL-fuzzy precontinuous, pairwise RL-fuzzy preirresolute mappings, and pairwise RL-fuzzy precompactness
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