Summary: In an attempt to show the way we pass from ordered semigroups to ordered \(\Gamma\)-hypersemigroups, we examine our results [Semigroup Forum 44, No. 3, 341--346 (1992; Zbl 0756.06008)] for an ordered \(\Gamma\)-hypersemigroup. It has been shown that the concept of semisimple ordered \(\Gamma\)-hypersemigroup \(S\) is identical with the concept ``the ideals of \(S\) are idempotent'' and the ideals of \(S\) are idempotent if and only if for all ideals \(A\), \(B\) of \(S\), we have \(A\cap B = (A\Gamma B]\). The main results of the paper are the following: The ideals of an ordered \(\Gamma\)-hypersemigroup \(S\) are weakly prime if and only if they form a chain and \(S\) is semisimple. The ideals of \(S\) are prime if and only if they form a chain and \(S\) is intraregular. It should be finally mentioned that the concepts ``prime ideal'' and ``both semiprime and weakly prime ideal'' are the same; and that in commutative ordered \(\Gamma\)-hypersemigroups the prime and weakly prime ideals coincide. For an abstract formulation of the above statements we refer to our paper [Turk. J. Math. 40, No. 2, 310--316 (2016; Zbl 1424.06052)].