Abstract
We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that <TEX>$S(k)=1$</TEX> for some <TEX>$k{\in}X$</TEX> 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 <TEX>$S(k)=1$</TEX> for some <TEX>$k{\in}X$</TEX> 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.
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