In this paper, we introduce the concepts of order-congruences and strong order-congruences on an ordered semihypergroup $S,$ and obtain the relationship between strong order-congruences and pseudoorders on $S.$ Furthermore, we characterize the (strong) order-congruences by the $\rho$-chains, where $\rho$ is a (strong) congruence on $S.$ Moreover, we give a method of constructing order-congruences, and prove that every hyperideal $I$ of an ordered semihypergroup $S$ is congruence class of one order-congruence on $S$ if and only if $I$ is convex. Finally, we define and study the strong order-congruence generated by a strong congruence. As an application of the results of this paper, we solve an open problem on ordered semihypergroups given by Davvaz et al.
TANG, JIAN; LUO, YANFENG; and XIE, XIANGYUN
"A study on (strong) order-congruences in ordered semihypergroups,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 40.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/40