Affiliations: [a] School of Mathematics and Statistics, Fuyang Normal University, Fuyang, P.R. China | [b] Department of Mathematics, Yazd University, Yazd, Iran
| [c] School of Mathematics and Computational Science, Wuyi University, Jiangmen, P.R. China | [d] Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Saudi Arabia
Correspondence:
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Corresponding author. Jian Tang, School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui
236037, P.R. China. Tel./Fax: +86 0558 2591133; E-mail: tangjian0901@126.com.
Abstract: In this paper, we introduce the concept of interior Γ-hyperideals of ordered Γ-semihypergroups, which is a generalization of the concept of interior Γ-hyperideals of Γ-semihypergroups to ordered Γ-semihypergroup theory, and investigate its related properties. Furthermore, we define and discuss the fuzzy interior Γ-hyperideals of ordered Γ-semihypergroups. In particular, we give the characterization of fuzzy interior Γ-hyperideal generated by a fuzzy subset in an ordered Γ-semihypergroup. In addition, we consider the concepts of (λ, μ)-fuzzy Γ-hyperideals and (λ, μ)-fuzzy interior Γ-hyperideals in ordered Γ-semihypergroups. Finally, we introduce the notion of (λ, μ)-fuzzy simple ordered Γ-semihypergroups and prove that an ordered Γ-semihypergroup is simple if and only if it is (λ, μ)-fuzzy simple. Especially, characterization of simple ordered Γ-semihypergroups in terms of (λ, μ)-fuzzy interior Γ-hyperideals is given.
