AbstractThe concept of fuzzy right multiplication Γ-semigroup is introduced by means of fuzzy right Γ-ideals, and some properties are investigated with the help of some classes of Γ-semigroups. It is shown that for any fuzzy right Γ-ideal ϑ of X, ϑ ⊆ X ◦Γ ϑ. More- over, if a Γ-semigroup X is simple with a ∈ aΓX for every a ∈ X, then X is a fuzzy right multiplication Γ-semigroup.