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 ...

This study applies the hyperstructure theory to BF-algebra, which is an algebraic structure. In fact, we define hyper-BF-algebras and hyper-BF ideals investigate several of their related characteristics. BF-algebra ideal characteristics are taken into account, supported examples built. Here, also develop new concepts known as hyper-B-algebra, hyper-BG-algebra, hyper-BH algebra generalizations o...

The foldness of PI( , ⊆, ⊆)BCK -ideals and PI( , , )BCK -ideals is considered. The fuzzy version of such notions is also discussed.

We study hyper pseudo BCC-algebras which are a common generalization of and BCK-algebras. In particular, we introduce different notion describe the relationship among them. Then, by choosing one these definitions, investigate for its related properties.