Abstract
We have introduced and discussed in a recent paper [2] various sublattices such as L f , L t , and L f n t , of the lattice L of fuzzy subgroups of a given group. In particular, we proved that the sublattice L f n , 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 Ln 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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