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The concept of fuzzy right multiplication \( \Gamma \)-semigroup is introduced by means of fuzzy right \( \Gamma \)-ideals, and some properties are investigated with the help of some classes of \( \Gamma \)-semigroups. It is shown that for any fuzzy right \( \Gamma \)-ideal \( \vartheta \) of \( X \), \( \vartheta^{2} \subseteq X \circ_{\Gamma} \vartheta \). Moreover, if a \( \Gamma \)-semigroup \( X \) is simple with \( a \in a\Gamma X \) for every \( a \in X \), then \( X \) is a fuzzy right multiplication \( \Gamma \)-semigroup.
