Abstract
In this paper, we study the connection between generalized quasi-left alter BCI-algebra and commutative Clifford semigroup by introducing the concept of an adjoint semigroup. We introduce QM-BCI algebra, in which every element is a quasi-minimal element, and prove that each QM-BCI algebra is equivalent to generalized quasi-left alter BCI-algebra. Then, we introduce the notion of generalized quasi-left alter-hyper BCI-algebra and prove that every generalized quasi-left alter-hyper BCI-algebra is a generalized quasi-left alter BCI-algebra. Next, we propose a new notion of quasi-hyper BCI algebra and discuss the relationship among them. Moreover, we study the subalgebras of quasi-hyper BCI algebra and the relationships between Hv-group and quasi-hyper BCI-algebra, hypergroup and quasi-hyper BCI-algebra. Finally, we propose the concept of a generalized quasi-left alter quasi-hyper BCI algebra and QM-quasi hyper BCI-algebra and discuss the relationships between them and related BCI-algebra.
Highlights
In 1966, Japanese mathematicians Imai and Iseki proposed the concepts of BCK/BCIalgebra based on logical algebra and the algebraic expression of combinators in combinatorial logic, which are the two kinds of algebraic structures closest to combinatorial logic, fuzzy logic, etc.) [1,2,3,4,5]
We prove that generalized quasi-left alter BCI-algebra, QM-BCI algebra and generaized quasi-left alter hyper BCI-algebra are equivalent to one another
We introduced QM-BCI algebra and proved that the generalized quasi-left alter BCI-algebra is equivalent to QM-BCI algebra
Summary
In 1966, Japanese mathematicians Imai and Iseki proposed the concepts of BCK/BCIalgebra based on logical algebra and the algebraic expression of combinators in combinatorial logic, which are the two kinds of algebraic structures closest to combinatorial logic, fuzzy logic, etc.) [1,2,3,4,5]. Iseki in 1980 [6]; generalized associative BCI-algebra proposed by Tiande Lei in 1985 [7]; generalized quasi-left alter BCI-algebra by X.H. Zhang in 1992 [8]; the mixed structure of BCI-algebra and semigroup [9]. In 2021, Y.D. Du and X.H. Zhang introduced the definition of hyper BZ-algebra and discuss the relationships between it and semihypergroups by an adjoint semigroup ([32]). We introduce the concepts of generalized quasi-left alter quasi-hyper BCI-algebra and QM-quasi-hyper BCI-algebra and discuss the relationships between them and the related BCI-algebra
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
