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