We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.