Bases of fuzzy vector spaces. (English) Zbl 0797.46060

Author’s abstract. Let \(V\) be a vector space over a field \(F\). Let \(A\) be a fuzzy subspace of \(V\) over \(F\). We give sufficient conditions for \(A\) to have a basis over a fuzzy subfield \(K\) of \(F\). We also show that if \(A\) has the sup property, then \(A\) has a fully free basis over \(F\) but not necessarily a fully free basis over \(K\).


46S40 Fuzzy functional analysis
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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