This paper is devoted to counting distinct fuzzy subgroups (DFS) of finite dihedral group D2n, where n is a product of finite number of distinct primes, with respect to the equivalence relation ≈ . This counting has connections with familiar integer sequence called ordered Bell numbers. Furthermore, a recurrence relation and generating function was derived for counting DFS of D2n.
In this paper, we give an explicit formula for counting the number of distinct fuzzy sub-groups of dihedral group D2ps for any prime(p) and any integer s≥1. This we achieved using the algorithm described on the most recent equivalence relation ≈ known in the literature to classify fuzzy groups.
