  In order to study the structure of $A^+(B_n)$ -- the affine near-semiring
over a Brandt semigroup -- this work completely characterizes the Green's
classes of its semigroup reducts. In this connection, this work characterizes
the elements of $A^+(B_n)$ and reports the size of $A^+(B_n)$. Further,
idempotents and regular elements of the semigroup reducts of $A^+(B_n)$ have
also been characterized and studied some relevant semigroups in $A^+(B_n)$.
