On the structure of fuzzy groups


The structure of fuzzy groups is examined. We characterize products and weak products of fuzzy (abelian) groups in terms of canonical homomorphisms. We give a characterization of fuzzy internal direct sums in terms of a generating fuzzy set, and show that the internal direct sum is isomorphic to the external direct sum. We give a characterization of free (abelian) fuzzy groups that is more general and more elegant than that of [G-M]. We define the notion of a cyclic fuzzy group, and show that finitely generated fuzzy groups are direct sums of cyclic fuzzy groups.

Publication Title

International Conference on Fuzzy Theory and Technology Proceedings, Abstracts and Summaries

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