Abstract
Let V denote a vector space over a field F and let A denote a fuzzy subspace of V over a fuzzy subfield K of F. Let X be a fuzzy subset of V such that X ⊆ A and let 〈X〉 denote the intersection of all fuzzy subspaces of V over K that contain X and are contained in A. We characterize the fuzzy subspace 〈X〉 of A over K. We use this result to introduce the concept of fuzzy freeness of a fuzzy subset X of V and characterize it in terms of linear independence in the usual sense.
| Original language | English |
|---|---|
| Pages (from-to) | 271-281 |
| Number of pages | 11 |
| 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 vector spaces. / Malik, Davender S.; Mordeson, John N.
In: Information Sciences, Vol. 55, No. 1-3, 1991, p. 271-281.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Fuzzy vector spaces
AU - Malik, Davender S.
AU - Mordeson, John N.
PY - 1991
Y1 - 1991
N2 - Let V denote a vector space over a field F and let A denote a fuzzy subspace of V over a fuzzy subfield K of F. Let X be a fuzzy subset of V such that X ⊆ A and let 〈X〉 denote the intersection of all fuzzy subspaces of V over K that contain X and are contained in A. We characterize the fuzzy subspace 〈X〉 of A over K. We use this result to introduce the concept of fuzzy freeness of a fuzzy subset X of V and characterize it in terms of linear independence in the usual sense.
AB - Let V denote a vector space over a field F and let A denote a fuzzy subspace of V over a fuzzy subfield K of F. Let X be a fuzzy subset of V such that X ⊆ A and let 〈X〉 denote the intersection of all fuzzy subspaces of V over K that contain X and are contained in A. We characterize the fuzzy subspace 〈X〉 of A over K. We use this result to introduce the concept of fuzzy freeness of a fuzzy subset X of V and characterize it in terms of linear independence in the usual sense.
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UR - http://www.scopus.com/inward/citedby.url?scp=0026177617&partnerID=8YFLogxK
U2 - 10.1016/0020-0255(91)90018-P
DO - 10.1016/0020-0255(91)90018-P
M3 - Article
VL - 55
SP - 271
EP - 281
JO - Information Sciences
JF - Information Sciences
SN - 0020-0255
IS - 1-3
ER -