A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzysp-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 fuzzysp-continuous (resp., fuzzysp-open) mapping and other stronger forms ofsp-continuous (resp., fuzzysp-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 fuzzysp-connected. Counter examples are given to show the noncoincidence of these sets and mappings.