Affiliations: [a] Department of Mathematics, Yazd University, Yazd, Iran
| [b] Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, Thailand
| [c] Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen, Thailand
Correspondence:
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Corresponding author. Nareupanat Lekkoksung, Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand. E-mail: [email protected].
Abstract: Ideals play an essential part in studying ordered semigroups. There are several generalizations of ideals that are used to investigate ordered semigroups. It is known that (m, n)-ideals are an abstraction of bi-ideals, and n-interior ideals are an abstraction of interior ideals. This paper introduces a generality of (m, n)-ideals and n-interior ideals, so-called (α, β)-fuzzy (m, n)-ideals and (α, β)-fuzzy n-interior ideals. Furthermore, we discuss our current notions with those that already exist. We examine connections between (m, n)- (resp., n-interior) ideals and (α, β)-fuzzy (m, n)- (resp., n-interior) ideals. A characterization of (α, β)-fuzzy (m, n)- (resp., n-interior) ideals, by a particular product, in ordered semigroups is provided. We demonstrate that our results generalize the known results through specific settings.
