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FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS.

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In this paper, we study an equivalence relation on the set ot tuzzy subgroups of an arbitrary group G and give four equivalent conditions each oi which characterizes this relation. We demonstrate that with this equivalence relation each equivalence class constitutes a lattice under the ordering of fuzzy set inclusion. Moreover, we study the behavior of these equivalence classes under the action of a group homomorphism.

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