In this paper, we classify distinct fuzzy subgroups of dihedral groups of order and for distinct primes p and q, under the natural equivalence relation of fuzzy subgroups defined in [2] and a special algorithm proposed and studied in [3]. In the process, we present formulae for (i) the number of maximal chains and (ii) the number of distinct fuzzy subgroups of these groups. Our ultimate aim is to classify distinct fuzzy subgroups of the dihedral group  p and q are distinct primes, but this classification problem cannot be accomplished in a single paper. This paper is a precursor to a sequel of papers that will lead to the general result.

dihedral group, equivalence, fuzzy subgroup, maximal chains, cyclic flag, d-cyclic, 2d-cyclic, 3d-cyclic, b-cyclic.