  This work investigates the rank properties of $A^+(B_n)$, the multiplicative
semigroup reduct of the affine near-semirings over an aperiodic Brandt
semigroup $B_n$. In this connection, the work obtains the small rank, lower
rank and large rank of $A^+(B_n)$. Further, the work provides lower bounds for
intermediate rank and upper rank of $A^+(B_n)$.
