B-algebra is an algebraic structure related to BCI/BCK-algebra. Many researchers have studied fuzzy B-ideal on B-algebra, m-polar fuzzy set on BCI-algebra and B-algebra, m-polar fuzzy subalgebra on BCI-algebra and B-algebra, m-polar fuzzy ideal on BCI-algebra, m-polar (∈, ∈)-fuzzy p-ideal on BCI-algebra, m-polar (∈, ∈) -fuzzy q-ideal on BCI-algebra, and m-polar (∈, ∈)-fuzzy a-ideal on BCI-algebra. By combining some of these structures, we build a new structure, namely m-polar (∈, ∈) -fuzzy B-ideal on B-algebra. In this research, we investigate and describe the properties of m-polar (∈, ∈)-fuzzy B-ideal. We also investigate  the connection among m-polar (∈, ∈) -fuzzy B-ideal, m-polar fuzzy subalgebra, and m-polar fuzzy ideal. We serve a condition that causes an m-polar fuzzy ideal to become an m-polar m-polar (∈, ∈) -fuzzy B-ideal. Futhermore, we also serve expansion properties of an m-polar  (∈, ∈)-fuzzy B-ideal.