On Generalized Compactness in Fuzzy Bitopological Spaces

Abstract

The main objective of this research is to study some types of generalized closed sets in fuzzy bitopology including $(i,j)-g\alpha-cld$, $(i,j)-gs-cld$, $(i,j)-gp-cld$, and $(i,j)-g\beta-cld$. We then present basic theorems for determining their relationships and explain their properties, such as closure and interior. In addition, there are many interesting counterexamples. The last part of the research focuses on generalized compactness in fuzzy bitopological spaces and their types and explores the relationships between these concepts, their important theories, and some relevant counterexamples. The results established in this paper are new in the domain of fuzzy bitopology.