First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${ ho};o;{sigma}{in}$ FC(S) for any two fuzzy congruences ${ ho};and;{sigma}$ on a fuzzy groupoid ($S,{odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.