We have introduced and discussed in a recent paper  various sublattices such as L f , L t , and L fnt of the lattice L of fuzzy subgroups of a given group. In particular, we proved that the sublattice L fnt of fuzzy normal subgroups with finite range and tip t is a modular sublattice of L. Here, we remove all the restrictions on the choice of fuzzy normal subgroups, and prove that the class of all fuzzy normal subgroups L n forms the modular sublattice of L. As a tool, we prove an important result that the fuzzy subgroups generated by a pair of fuzzy normal subgroups of a group is fuzzy normal.
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