Abstract
In this paper, some fundamental relationships of a Gamma-semihypergroup and its operator semihypergroup in terms of fuzzy subsets, fuzzy hyperideals and fuzzy hyperideal extension are obtained. Using these in obtaining some characterization theorems of Gamma-semihypergroups in terms of fuzzy subsets, we highlight the effectiveness of operator semihypergroups in the study of Gamma-semihypergroups in terms of fuzzy subsets.