The membership dimension of a fuzzy subspace (Q2710047)

Properties of fuzzy vector spaces and fuzzy congruences are well-known e.g. from the following papers: \textit{A. K. Katsaras} and \textit{D. B. Liu} [J. Math. Anal. Appl. 58, 135-146 (1977; Zbl 0358.46011)]; \textit{R. Lowen} [Fuzzy Sets Syst. 3, 291-310 (1980; Zbl 0439.52001)]; \textit{P. Lubczonok} [ibid. 38, No. 3, 329-343 (1990; Zbl 0727.15002)]; \textit{R. Kumar} [ibid. 45, No. 1, 109-116 (1992; Zbl 0747.15001)]; \textit{N. Kuroki} [Inf. Sci. 60, No. 3, 247-259 (1992; Zbl 0747.20038)]; \textit{S. Li} [J. Fuzzy Math. 3, No. 3, 633-636 (1995; Zbl 0847.15001)]; \textit{T. Lu} and \textit{W. Gu} [ibid. 3, No. 4, 921-931 (1995; Zbl 0844.15004)]. The author rediscovers some of these properties and introduces his own terminology. The title ``membership dimension'' is connected with the maximal chain of level subspaces.