On the number of fuzzy subgroups of dicyclic groups

摘要

One of the significant aspects of fuzzy group theory is classification of the fuzzy subgroups of finite groups under a suitable equivalence relation. In this paper, we determine the number of distinct fuzzy subgroups of dicyclic groups in some particular cases by the new equivalence relation introduced by Tǎrnǎuceanu. In this case, the corresponding equivalence classes of fuzzy subgroups of a group G are closely connected to the automorphism group and the chains of subgroups of G. In fact, this new equivalence relation generalizes the natural equivalence relation defined on the lattice of fuzzy subgroups.