New Generalized Separation Axioms Structures in Fuzzy Bitopological Spaces
摘要
This work aims to enhance several mathematical concepts within fuzzy bitopological spaces by analyzing various fuzzy separation axioms, such as \(T_h\) and \(T_{hw}\) , where \(h={0,1,2,{2_\frac{1}{2}}}\) . The study employs different types of fuzzy generalized closed sets of \((X,\delta _i,\delta _j)\) , including fuzzy \((i,j)-g\alpha \) -closed sets, fuzzy \((i,j)-gp\) -closed sets, fuzzy \((i,j)-gs\) -closed sets, and fuzzy \((i,j)-g\beta \) -closed sets, with \(i,j=\{1,2\}\) and \(i\ne j\) . After that, we give some important theorems that explain how they relate to each other and what their main characteristics are. These are followed by some strong counterexamples that show the inverse connection is not valid. This study’s conclusions are novel to the domain of fuzzy bitopological spaces. Furthermore, this work will serve as a valuable reference by introducing numerous fundamental concepts that remain unexplored.