On the number of fuzzy subgroups of finite abelian p-groups with type (pn, pm)

It is well known that a finite abelian group can be written as a direct product of p-groups. Therefor the problem of counting the fuzzy subgroups of finite abelian groups must be first solved for p-groups. In this paper, we determine the number of fuzzy subgroups of finite abelian p-groups with type (p
ⁿ
, p
^m
), and get explicit formula of it, where p is a prime and n is a natural number, m = 1, 2.