A BG-algebra is a non-empty set X with a binary operation ∗ and a constant 0 satisfying the following axioms: (B1) x∗x = 0, (B2) x∗0 = x, and (BG) (x ∗ y) ∗ (0 ∗ y) = x for any x; y ∈ X, which is a generalization of B-algebra, such that some of properties of BG-algebra have similarity by B-algebra such as (B1) and (B2). However, some of the concepts in B-algebra can also appl…