Motivated by Samet et al. [Nonlinear Anal., 75 (4) (2012), 2154- 2165], we introduce the notions of a-f-fuzzy contractive mapping and b-y-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.