U- BG - BH- algebra

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.