green's relations on ordered n-ary semihypergroups

In this paper, we introduce the concept of weak i-hyperfilters of ordered n-ary semihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, and discuss their related properties. we define green’s relations mi, j , h and k on ordered n-ary semihypergroups and investigate the relationships between green’s relations and the equivalence relation wi, which is generated by the weak i-hyperfilters. also, we give the characterizations of intra-regular ordered n-ary semihypergroups via the properties of weak ihyperfilters. finally, we introduce the concepts of (i-, λ-)duo ordered n-ary semihypergroups and establish some interesting properties.