---

In this book, we introduce a new class of a BH-algebra. We call this class a U-BG-BH-algebra, where U is a BG-algebra containing 0 with more than or equal one elements and it is contained in a BH-algebra. Also, we give the concepts of (a U-BG-ideal, a closed U-BG-ideal, a completely closed U-BG-ideal) of a U-BG-BH-algebra. And we study some related properties, the relationships between them and some other ideals of a BH-algebra in ordinary and fuzzy senses. On the other hand, we define (a U-BG-p-ideal, a U-BG-q-ideal and U-BG-strong-ideal) of a U-BG-BH-algebra and combine these types of U-BG-ideals with (a closed U-BG-ideal, a completely closed U-BG-ideal, a U-BG-p-ideal, a U-BG-q-ideal and U-BG-strong-ideal) of a U-BG-BH-algebra.

---

A Prof. Husein Hadi Abbass is the Dean Assistant post for Scientific Affairs in the Faculty of Computer Science and Mathematics university of Kufa - Iraq. He obtained master´s degree in applied mathematics from the Technology University in Iraq in 1995. He has publications in Algebra, MV-algebra,Image Processing ,Algebraic Statistics,Fuzzy maths

---