QM-BZ-Algebras and Quasi-Hyper BZ-Algebras

BZ-algebra, as the common generalization of BCI-algebra and BCC-algebra, is a kind important logic algebra. Herein, new concepts QM-BZ-algebra quasi-hyper BZ-algebra are proposed their structures constructions studied. First, definition presented, structure obtained: Each KG-union quasi-alter BCK-algebra anti-grouped BZ-algebra. Second, generalized quasi-left alter (hyper) BZ-algebras QM-hyper introduced, some characterizations them investigated. Third, proposed, relationships among hyper BCI-algebra, discussed. Finally, several special classes studied in depth following results proved: (1) an BZ-algebra; (2) every corresponds to semihypergroup.