### Abstract

It is shown that for a group G if σ_{μ} is a fuzzy subgroup of G for all fuzzy subgroups μ of G × G, then either G is a cyclic group of order p^{m} for some m ≥ 1 or G ∼- Z(p^{∞}), where p is a prime. Conversely, we prove that if either G is a cyclic group of order p^{m} for some m ≥ 1 or G ∼- Z(p^{∞}) then σ_{μ} is a fuzzy subgroup of G for any fuzzy subgroup μ, of G × G, where p is a prime.

Original language | English (US) |
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Pages (from-to) | 193-198 |

Number of pages | 6 |

Journal | Information sciences |

Volume | 56 |

Issue number | 1-3 |

DOIs | |

State | Published - Aug 1991 |

### All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Theoretical Computer Science
- Computer Science Applications
- Information Systems and Management
- Artificial Intelligence

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## Cite this

Malik, D. S., & Mordeson, J. N. (1991). A note on fuzzy relations and fuzzy groups.

*Information sciences*,*56*(1-3), 193-198. https://doi.org/10.1016/0020-0255(91)90030-X