Characterizations of generalized fuzzy ideals in ordered semigroups

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 (alpha, beta)-fuzzy (m, n)-ideals and (alpha, beta)-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 (alpha, beta)-fuzzy (m, n)- (resp., n-interior) ideals. A characterization of (alpha, beta)-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.