### 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 |

### Fingerprint

### 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

*Information Sciences*,

*55*(1-3), 271-281. https://doi.org/10.1016/0020-0255(91)90018-P

**Fuzzy vector spaces.** / Malik, Davender S.; Mordeson, John N.

Research output: Contribution to journal › Article

*Information Sciences*, vol. 55, no. 1-3, pp. 271-281. https://doi.org/10.1016/0020-0255(91)90018-P

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0026177617&partnerID=8YFLogxK

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 -