الخلاصة

The main purpose of this paper, The notions of norm and distance in BH-algebras are introduced, and some basic properties in normed BH-algebras are given. It is obtained that the isomorphic (homomorphic) image and inverse image of a normed BH-algebra are still normed BH-algebras. The relations of normed properties between BH-algebra and Cartesian product of BH-algebras are investigated. The limit notion of sequence of points in normed BH-algebras is introduced, and its related properties are investigated, the relations between bounded normed BH-algebras and fuzzy BH-algebras are discussed.