This paper introduces a new notion of algebra called BS-algebra and some of its properties are discussed in detail. Also, we define a S(a,b) of BS-algebra and discus of properties and theorems of it. Some of theorems of a new ideals of BS-algebra are introduced and proved. Also, we introduced some new types of ideals of Z-algebra and we linked these ideals with some theorems and properties. Also, we define the concept of pseudo Z-algebra and introduced some examples and new concepts in it, including the concept of pseudo b-subalgebra and introduced some theorems and properties in this new concepts.

In this paper, we present the idea in fuzzy V-B-ideal in V-B-ḄH algebra, we state and gives some propositions and examples which explain the relationships between these notions and the other types of fuzzy ideal s in ḄH algebra