### 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 |
---|---|

Pages (from-to) | 193-198 |

Number of pages | 6 |

Journal | Information Sciences |

Volume | 56 |

Issue number | 1-3 |

DOIs | |

State | Published - 1991 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Computer Science Applications
- Information Systems
- Information Systems and Management
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Statistics and Probability

### Cite this

*Information Sciences*,

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

**A note on fuzzy relations and fuzzy groups.** / Malik, Davender S.; Mordeson, John N.

Research output: Contribution to journal › Article

*Information Sciences*, vol. 56, no. 1-3, pp. 193-198. https://doi.org/10.1016/0020-0255(91)90030-X

}

TY - JOUR

T1 - A note on fuzzy relations and fuzzy groups

AU - Malik, Davender S.

AU - Mordeson, John N.

PY - 1991

Y1 - 1991

N2 - It is shown that for a group G if σμ is a fuzzy subgroup of G for all fuzzy subgroups μ of G × G, then either G is a cyclic group of order pm 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 pm for some m ≥ 1 or G ∼- Z(p∞) then σμ is a fuzzy subgroup of G for any fuzzy subgroup μ, of G × G, where p is a prime.

AB - It is shown that for a group G if σμ is a fuzzy subgroup of G for all fuzzy subgroups μ of G × G, then either G is a cyclic group of order pm 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 pm for some m ≥ 1 or G ∼- Z(p∞) then σμ is a fuzzy subgroup of G for any fuzzy subgroup μ, of G × G, where p is a prime.

UR - http://www.scopus.com/inward/record.url?scp=0026204053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026204053&partnerID=8YFLogxK

U2 - 10.1016/0020-0255(91)90030-X

DO - 10.1016/0020-0255(91)90030-X

M3 - Article

VL - 56

SP - 193

EP - 198

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

IS - 1-3

ER -