Role of operator semirings in characterizing $\mathrm{\Gamma }$-semirings in terms of fuzzy subsets

The operator semirings of a $\mathrm{\Gamma }$-semiring have been brought into use to study $\mathrm{\Gamma }$-semiring in terms of fuzzy subsets. This is accomplished by obtaining various relationships between the set of all fuzzy ideals of a $\mathrm{\Gamma }$-semiring and the set of all fuzzy ideals of its left operator semiring such as lattice isomorphism between the sets of fuzzy ideals of a $\mathrm{\Gamma }$-semiring and its operator semirings.