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

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Fuzzy Sets and Systems*,

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

**Fuzzy generators and fuzzy direct sums of Abelian groups.** / Malik, Davender S.; Mordeson, John N.; Nair, P. S.

Research output: Contribution to journal › Article

*Fuzzy Sets and Systems*, vol. 50, no. 2, pp. 193-199. https://doi.org/10.1016/0165-0114(92)90218-S

}

TY - JOUR

T1 - Fuzzy generators and fuzzy direct sums of Abelian groups

AU - Malik, Davender S.

AU - Mordeson, John N.

AU - Nair, P. S.

PY - 1992/9/10

Y1 - 1992/9/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249010031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249010031&partnerID=8YFLogxK

U2 - 10.1016/0165-0114(92)90218-S

DO - 10.1016/0165-0114(92)90218-S

M3 - Article

VL - 50

SP - 193

EP - 199

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

IS - 2

ER -