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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Corresponding author. Address correspondence to John N. Mordeson, Department of Mathematics and Computer Science, Creighton University, Omaha, Nebraska 68178.