Affiliations: [a]
School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P.R. China | [b]
Department of Mathematics, Yazd University, Yazd, Iran
| [c]
School of Mathematics and Computational Science, Wuyi University, Jiangmen, P.R. China
Correspondence:
[*]
Corresponding author. Xiangyun Xie, School of Mathematics and Computational Science, Wuyi University, Jiangmen,
Guangdong 529020, P.R. China. Tel./Fax: +86 0750 3296580; E-mail: xyxie@xyu.edu.cn.
Abstract: In this paper, as a generalization of the concept of quasi-Γ-hyperideals of Γ-semihypergroups to ordered Γ-semihypergroup theory, the concept of quasi-Γ-hyperideals of ordered Γ-semihypergroups is introduced, and related properties are discussed. Furthermore, we define and study fuzzy quasi-Γ-hyperideals of ordered Γ-semihypergroups. In particular, we investigate the structure of fuzzy quasi-Γ-hyperideal generated by a fuzzy subset in an ordered Γ-semihypergroup. In addition, we also introduce the concepts of completely prime, weakly completely prime and completely semiprime fuzzy quasi-Γ-hyperideals of ordered Γ-semihypergroups, and characterize bi-regular ordered Γ-semihypergroups in terms of completely semiprime fuzzy quasi-Γ-hyperideals. Finally, several characterizations of regular and intra-regular ordered Γ-semihypergroups by the properties of fuzzy quasi-Γ-hyperideals are given.
Keywords: Ordered Γ-semihypergroup, ordered fuzzy point, (fuzzy) quasi-Γ-hyperideal, weakly completely prime fuzzy quasi-Γ-hyperideal, completely semiprime fuzzy quasi-Γ-hyperideal
