AbstractIn this section, we introduce the notions of a left and a right translational invariant fuzzy subsets of a Γ−semigroup M, as well as the concept of a unit with respect to a fuzzy subset, and study their properties. We also prove that if μ is a translational invariant fuzzy subset of a commutative Γ−semigroup with unity, then the principal ideal generated by an element and μ that contains a unity element is a prime ideal of the Γ−semigroup.