Relations between G-sets and their associate G^{hat}-sets

In this paper, we define and consider $G$-set on$Gamma$-semihypergroups and we obtain relations between $G$-setsand their associate $widehat{G}$-sets where $G$ is a$Gamma$-semihypergroup and $widehat{G}$ is an associatedsemihypergroup. Finally, we obtain the relation between direct limit of $widehat{G}$-sets from the direct limit defined on $G$-sets.