  The purpose of this paper is to determine the number of fuzzy subgroups of a
finite abelian group of order $p^{n}q^{m}$. As an application of our main
result, explicit formulas for the number of fuzzy subgroups of
$\mathbb{Z}_{p}^{n}\times\mathbb{Z}_{q}^{m}$ and
$\mathbb{Z}_{p^{n}}\times\mathbb{Z}_{q}^{m}$ are given.
