### Abstract

We define the concept of a fuzzy generating set and describe the fuzzy subgroup which it generates. We introduce the notion of a minimal fuzzy generating set and we show that any fuzzy subgroup whose support is cyclic has a minimal fuzzy generating set. We show by examples that this result breaks down if the support of A is a direct sum of two or more cyclic groups. These examples also show that a fuzzy subgroup of a group G need not be a fuzzy direct sum of subgroups whose supports are cyclic even if G is a direct sum of cyclic groups. We show that every fuzzy subgroup is a fuzzy direct sum of p-primary fuzzy subgroups.

Original language | English (US) |
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Pages (from-to) | 193-199 |

Number of pages | 7 |

Journal | Fuzzy Sets and Systems |

Volume | 50 |

Issue number | 2 |

DOIs | |

State | Published - Sep 10 1992 |

### All Science Journal Classification (ASJC) codes

- Logic
- Artificial Intelligence

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## Cite this

Malik, D. S., Mordeson, J. N., & Nair, P. S. (1992). Fuzzy generators and fuzzy direct sums of Abelian groups.

*Fuzzy Sets and Systems*,*50*(2), 193-199. https://doi.org/10.1016/0165-0114(92)90218-S