Fuzzy vector spaces

D. S. Malik; John N. Mordeson

doi:10.1016/0020-0255(91)90018-P

Fuzzy vector spaces

D. S. Malik, John N. Mordeson

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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	https://doi.org/10.1016/0020-0255(91)90018-P
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

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10.1016/0020-0255(91)90018-P

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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.",

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AU - Malik, D. S.

AU - Mordeson, John N.

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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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JF - Information Sciences

SN - 0020-0255

IS - 1-3

ER -

Fuzzy vector spaces

Abstract

All Science Journal Classification (ASJC) codes

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