\(I\)-\textbf{FTOP} is isomorphic to \(I\)-\textbf{FQN} and \(I\)-\textbf{AITOP}
The author gives two characterizations of \(I\)-FTOP, the cateogry of \(I\)-fuzzy topological spaces and \(I\)-fuzzy continuous mappings. Following the idea of quasi-coincident neighborhood systems introduced by the reviewer [J. Math. Anal. Appl. 76, 571--599 (1980; Zbl 0447.54006)], the author constructs the category of \(I\)-fuzzy quasi-coincident neighborhood spaces and their continuous mappings, denoted by \(I\)-FQN. Though the intuitions underlying \(I\)-FQN and \(I\)-FTOP are quite different, however, the author shows that \(I\)-FTOP is isomorphic to \(I\)-FQN. Second, the author constructs the category of antichain \(I\)-topological spaces and their continuous mappings, denoted \(I\)-AITOP, and shows that \(I\)-FTOP is isomorphic to \(I\)-AITOP.
scientific article; zbMATH DE number 2118383
scientific article