Title

On the structure of fuzzy groups

Abstract

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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