In this paper we shows that in ordered groupoids the Q-fuzzy right (resp. Q-fuzzy left) ideals are Q-fuzzy quasi-ideals, in ordered semigroups the Q-fuzzy quasi-ideals are Q-fuzzy bi-ideals, and in regular ordered semigroups the Q-fuzzy quasi-ideals and the Q-fuzzy bi-ideals coincide and show that if S is an ordered semigroup, then a Q-fuzzy subset f is a Q-fuzzy quasi-ideal of S if and only if there exist a Q-fuzzy right ideal g and a Q-fuzzy left ideal h of S such that f = g ∩ h.
In this paper, the concepts of hybrid pure hyperideals in ordered hypersemigroups are introduced and some algebraic properties of hybrid pure hyperideals are studied. We characterize weakly regular ordered hypersemigroups in terms of hybrid pure hyperideals. Finally, we introduce the concepts of hybrid weakly pure hyperideals and prove that the hybrid hyperideals are hybrid weakly pure hyperideals if such hybrid hyperideals satisfy the idempotent property.
Ideals play an essential part in studying ordered semigroups. There are several generalizations of ideals that are used to investigate ordered semigroups. It was known that (m, n)-ideals and n-interior ideals are an abstraction of bi-ideals and interior ideals, respectively. 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.