1Department of Computer Science, University of Bojnord, Bojnord, Iran
2Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. Hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. The Main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group G Z p1 Z p 2 Z p 3 Z pk = ´ ´ ´´ , where k p , p ,..., p 1 2 are distinct prime numbers. We introduce a very simple recursive formula to count the number of subgroups of G.