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.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

New Generalized Separation Axioms Structures in Fuzzy Bitopological Spaces

  • Ahlam Ahmed Alharbi,
  • Adem Kilicman

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.