N. Rakhsh Khorshid - Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran
S. Ostadhadi-Dehkordi - Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran

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.

Gamma-semihypergroup, G-set, G^{hat}-set, direct limit