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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.