On fuzzy \(sp\)-open sets (Q538203)

Summary: A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzy \(sp\)-open sets, is introduced, and their properties are studied and the relationship between this new concept and other weaker forms of fuzzy open sets are discussed. Moreover, we introduce fuzzy \(sp\)-continuous (resp., fuzzy \(sp\)-open) mappings and other stronger forms of \(sp\)-continuous (resp., fuzzy \(sp\)-open) mappings and establish their various characteristic properties. Finally, we study the relationships between all these mappings and other weaker forms of fuzzy continuous mappings and introduce fuzzy \(sp\)-connectedness. Counter examples are given to show the noncoincidence of these sets and mappings.