On (m, n)-hyperquasi-ideals of (fuzzy) hypersemigroups

In this note we introduce the notations of (m, n)hyperquasi-ideals, m-left hyperideals, n-right hyperideals in hypersemigroups. Some representation theorems about minimal (m, n)-hyperquasiideals, minimal m-left hyperideals, minimal nright hyperideals in hypersemigroups are obtained. Also, some properties of (m, n)-hyperquasiideals of hypersemigroups have been studied. Finally, (m, n)-quasisimple, m-left simple, n-right simple hypersemigroups are investigated. As an application of the results of this note, we can generalize that to fuzzy hypetquasiideals on fuzzy hypersemigroups.