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Using the idea of the commutator of two fuzzy subsets of a group introduced in the paper, the notion of the 'derived chain' of a fuzzy subgroup is introduced. A definition of a 'solvable fuzzy subgroup' is proposed and some properties of solvable fuzzy subgroups are discussed.
The 'commutator' of two fuzzy subsets of a group is defined and its properties are studied. Using this idea, the 'descending central chain' of a fuzzy subgroup is introduced. A definition of a nilpotent fuzzy group is proposed and different properties of nilpotent fuzzy groups are discussed.
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