Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585319120230801Green's relations on ordered n-ary semihypergroups14316710385810.48308/cgasa.19.1.143ENJukkrit DaengsaenDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.Sorasak LeeratanavaleeDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.0000-0001-8818-6134Journal Article20230421In this paper, we introduce the concept of weak $i$-hyperfilters of ordered $n$-ary<br />semihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, and then discuss their<br />related properties. We define the Green’s relations $M_i, J , H$ and $K$ on ordered $n$-ary<br />semihypergroups and investigate the relationships between the Green’s relations and the<br />equivalence relation $W_i$, which is generated by the weak $i$-hyperfilters. Also, we give<br />the characterizations of intra-regular ordered $n$-ary semihypergroups via the properties<br />of weak $i$-hyperfilters. Finally, we introduce the concepts of $(i-, Λ-)$duo ordered $n$-ary<br />semihypergroups and establish some interesting properties.https://cgasa.sbu.ac.ir/article_103858_f6acfd659d49b01664cafc06a330d3a9.pdf