Bolet´ ın de Matem´ aticas 25(2) 77–99 (2018) 77 Ordered Semihypergroup Constructions Construcciones de Semihipergrupos Ordenados L. Kamali Ardekani 1, a , B. Davvaz 2, b Abstract. The concept of ordered semihypergroups is a generalization of the concept of ordered semigroups. In this paper, we study some aspects of hyperideals, bi-hyperideals and quasi-hyperideals of ordered semihypergroups. We investigate the notions of regular, intra-regular and completely regular ordered semihypergroups and give their characterizations in terms of hyper- ideals, bi-hyperideals and quasi-hyperideals. Also, the notion of duo ordered semihypergroups is introduced and some related results are discussed. Keywords: Ordered semihypergroup, hyperideal, completely regular, duo ordered semihypergroup, bi-hyperideal, intra-regular, quasi-hyperideal. Resumen. El concepto de semihipergrupos ordenados es una generalizaci´ on del concepto de semigrupos ordenados. En este trabajo, estudiamos algunos aspectos de hiperideales, bi-hiperideales y cuasi hiperideales de semihipergru- pos ordenados. Investigamos las nociones de semihipergrupos ordenados re- gulares ideales, intra-regulares y completamente regulares y damos sus carac- terizaciones en t´ erminos de hiperideales, bi-hiperideales y cuasi-hiperideales. Adem´ as, se introduce la noci´ on de semihipergrupos ordenados d´ uo y se dis- cuten algunos resultados relacionados. Palabras claves: Semihipergrupo ordenado, hiperideal, completamente regu- lar, semihipergrupo ordenado d´ uo, bi-hiperideal, intra-regular, cuasi-hiperideal. Mathematics Subject Classification: 06F05, 20N20. Recibido: febrero de 2018 Aceptado: febrero de 2019 1. Introduction Ordered semigroups have been studied by many authors, for example [1, 4, 12, 13, 16, 17, 19, 18, 23, 24]. In [10], Kehayopulu defined the ideal and weakly prime ideal in po-semigroup (: ordered semigroups). Completely regular poe- semigroups (: ordered semigroups having a greatest element) have been con- sidered by Kehayopulu in [11]. She showed the similarity between the theory of semigroups based on ideals and the theory of ordered semigroups based 1 Faculty of Engineering, Ardakan University, Ardakan, Iran 2 Department of Mathematics, Yazd University, Yazd, Iran a l.kamali@ardakan.ac.ir b davvaz@yazd.ac.ir