In this paper, first we introduce the notions of an (m,n)-hyperideal and a generalized (m,n)-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize (m,n)-regularity, (m,0)-regularity, and (0,n)-regularity of an ordered semihypergroup in terms of its (m,n)-hyperideals, (m,0)-hyperideals and (0,n)-hyperideals, respectively. The relations {_mmathcal{I}}, mathcal{I}_n, mathcal{H}_m^n, and mathcal{B}_m^n on an ordered semihypergroup are, then, introduced. We prove that mathcal{B}_m^n subseteq mathcal{H}_m^n on an ordered semihypergroup and provide a condition under which equality holds in the above inclusion. We also show that the (m,0)-regularity [(0,n)-regularity] of an element induce the (m,0)-regularity [(0,n)-regularity] of the whole mathcal{H}_m^n-class containing that element as well as the fact that (m,n)-regularity and (m,n)-right weakly regularity of an element induce the (m,n)-regularity and (m,n)-right weakly regularity of the whole mathcal{B}_m^n-class and mathcal{H}_m^n-class containing that element, respectively.
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