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 |
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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
Fuzzy primary representations of fuzzy ideals. / Malik, Davender S.; Mordeson, John N.
In: Information Sciences, Vol. 55, No. 1-3, 1991, p. 151-165.Research output: Contribution to journal › Article
}
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
VL - 55
SP - 151
EP - 165
JO - Information Sciences
JF - Information Sciences
SN - 0020-0255
IS - 1-3
ER -