### 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 (US) |
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Pages (from-to) | 151-165 |

Number of pages | 15 |

Journal | Information sciences |

Volume | 55 |

Issue number | 1-3 |

DOIs | |

State | Published - Jun 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). Fuzzy primary representations of fuzzy ideals.

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