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 |
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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 generators and fuzzy direct sums of Abelian groups. / Malik, Davender S.; Mordeson, John N.; Nair, P. S.
In: Fuzzy Sets and Systems, Vol. 50, No. 2, 10.09.1992, p. 193-199.Research output: Contribution to journal › Article
}
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.
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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 -