A Recursive Formula for the Number of Fuzzy Subgroups of Finite Cyclic Groups

Fuzzy groups and fuzzy theory have a lot of applications in several sciencessuch as mathematics, computer science, computer and electrical engineering.Hence, counting the number of fuzzy subgroups of finite groups to classify them isan important issue in fuzzy theory. The Main goal of this paper is to give an explicitformula for the number of fuzzy subgroups of a finite cyclic groupG=Z p1 x Z p2 x Z p3 x ... x Zp4, where P1, P2, ... Pk are distinct prime numbers.We introduce a very simple recursive formula to count the number of subgroups of G.

Keywords:

Fuzzy groups , Lattice , Finite cyclic groups , Chains