### 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 (US) |
---|---|

Pages (from-to) | 271-281 |

Number of pages | 11 |

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

## Fingerprint Dive into the research topics of 'Fuzzy vector spaces'. Together they form a unique fingerprint.

## Cite this

Malik, D. S., & Mordeson, J. N. (1991). Fuzzy vector spaces.

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