Spanning properties for fuzzy matroids (Q1311741)

Different results from matroid theory are surveyed and their fuzzy counterparts are investigated. The results of this paper are a direct continuation of a previous publication of the authors, see \textit{R. Goetschel} and \textit{W. Voxman} [Fuzzy Sets Syst. 27, No. 3, 291-302 (1988; Zbl 0651.05024)]. Some of the theorems are directly deduced from results reported in the previous paper. They provide important properties of the span of a fuzzy set, the fuzzy rank and the spike. The independence of fuzzy sets is characterized. Possible areas of application of the theoretical results are discussed.