Bases of fuzzy vector spaces. (English) Zbl 0797.46060

Mordeson, John N.

Inf. Sci. 67, No. 1-2, 87-92 (1993).

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 \(K\).

Reviewer: J.Albrycht (Poznań)

MSC:

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

Keywords:

fuzzy subspace; basis over a fuzzy subfield; fully free basis

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