Hatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60003320220801Applications of states to BI-algebras4563154391ENA.RezaeiDepartment of Mathematics, Payame Noor University, P.O.Box. 19395-3697, Tehran, IranS.SoleymaniDepartment of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, IranJournal Article20220803This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebras. We define state ideals on BI-algebras and give a characterization of the least state ideal of a BI-algebra. It is proved that the kernel of a Bosbach state on a BI-algebra X is an ideal of X. Further, by these concepts, we introduce the notions of state BI-algebras and state-morphism BI-algebras. The notion of complement pairs of a BI-algebra X is defined, and proves that under suitable conditions, there is a one-to-one correspondence between complement pairs of BI-algebras and state-morphism operators on BI-algebras.<br /> http://jahla.hatef.ac.ir/article_154391_d4aee9a51e3336ea763dd9eb6b2711d9.pdf