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) |
|---|---|
| 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