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 ...

The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.

By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and wecarry out a study on characterization of MV-algebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one non-isomorphic MV-algebra of orders $2$, $3$, $5$ and $7$ and two non-isomorphic MV-algebras of orders $4$ and $6$.

In this paper, we introduce the notion of hyper pseudo B C K - algebras, which is a generalization of pseudo BCK -algebras and hyper BCK -algebras and we investigates some related properties. In follow, we de ne some kinds of hyper pseudo BCK -ideals of a hyper pseudo BCK - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BCK -ideals of type 4 generated by...

In this paper, we introduce the notion of fuzzy obstinate ideals in MV -algebras. Some properties of fuzzy obstinateideals are given. Not only we give some characterizations of fuzzy obstinate ideals, but also bring the extension theorem of fuzzy obstinate ideal of an MV -algebra A. We investigate the relationships between fuzzy obstinate ideals and the other fuzzy ideals of an MV -algebra. We ...

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

In this paper we introduce the concepts of hyper P -semisimple Ialgebra and Abelian hyper I-algebra and we state and prove some related results. The hyper p-semi simple I-algebras is a generalization of p-semisimple BCI-algebras and a subclass of hyper I-algebras. Specially we show that every Abelian hyper I-algebra is a hyper psemisimple I-algebra and a commutative canonical hypergroup. In fol...

Any MV-algebra M can be embedded as a lattice in the Boolean algebra B(M) that is R-generated by M . We relate the study of states on an MV-algebra M to the study of finitely additive probabilities on B(M). In particular, we show that each state on M can be uniquely extended to a finitely additive probability on B(M). In case that M is a PMV-algebra, the conditional state s(a|b) defined for a, ...