### Abstract

Let R be a commutative ring with identity, and let A be a fuzzy ideal of R. Then A is said to have a fuzzy primary representation if A is the intersection of a finite number of fuzzy primary ideals. We show that every fuzzy ideal A of R such that A(0) = 1 has a fuzzy primary representation if and only if R is artinian. We show that uniqueness properties for reduced primary representations of ideals (in the usual sense) carry over to fuzzy ideals.

Original language | English |
---|---|

Pages (from-to) | 151-165 |

Number of pages | 15 |

Journal | Information Sciences |

Volume | 55 |

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*,

*55*(1-3), 151-165. https://doi.org/10.1016/0020-0255(91)90011-I

**Fuzzy primary representations of fuzzy ideals.** / Malik, Davender S.; Mordeson, John N.

Research output: Contribution to journal › Article

*Information Sciences*, vol. 55, no. 1-3, pp. 151-165. https://doi.org/10.1016/0020-0255(91)90011-I

}

TY - JOUR

T1 - Fuzzy primary representations of fuzzy ideals

AU - Malik, Davender S.

AU - Mordeson, John N.

PY - 1991

Y1 - 1991

N2 - Let R be a commutative ring with identity, and let A be a fuzzy ideal of R. Then A is said to have a fuzzy primary representation if A is the intersection of a finite number of fuzzy primary ideals. We show that every fuzzy ideal A of R such that A(0) = 1 has a fuzzy primary representation if and only if R is artinian. We show that uniqueness properties for reduced primary representations of ideals (in the usual sense) carry over to fuzzy ideals.

AB - Let R be a commutative ring with identity, and let A be a fuzzy ideal of R. Then A is said to have a fuzzy primary representation if A is the intersection of a finite number of fuzzy primary ideals. We show that every fuzzy ideal A of R such that A(0) = 1 has a fuzzy primary representation if and only if R is artinian. We show that uniqueness properties for reduced primary representations of ideals (in the usual sense) carry over to fuzzy ideals.

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UR - http://www.scopus.com/inward/citedby.url?scp=0026181448&partnerID=8YFLogxK

U2 - 10.1016/0020-0255(91)90011-I

DO - 10.1016/0020-0255(91)90011-I

M3 - Article

AN - SCOPUS:0026181448

VL - 55

SP - 151

EP - 165

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

IS - 1-3

ER -