Fuzzy \((\theta,s)\)-continuity and fuzzy \((\theta,s)\)-closed graphs (Q1314909)

The concept of \((\theta,s)\)-continuity is generalized in fuzzy setting which is independent with each of the notions fuzzy almost-continuity, fuzzy continuity, fuzzy semi-continuity and fuzzy \(\delta\)-continuity. It is investigated that fuzzy \((\theta,s)\)-continuity implies fuzzy weak continuity but the converse may not be true. It is seen that a \((\theta,s)\)-continuous function from a fuzzy topological space into a regular fuzzy topological space is fuzzy continuous and the image of a compact fuzzy topological space under a fuzzy \((\theta,s)\)-continuous surjective function is \(s\)-closed. Some characterizations of \((\theta,s)\)-continuous functions are studied. Finally, the concepts of fuzzy \((\theta, s)\)-closed graphs, fuzzy \((\theta, s)\)-\(T_ 2\)-spaces and fuzzy Urysohn spaces are introduced and their connections with fuzzy \((\theta, s)\)-continuity are investigated.