Zhang, Shaoyu; Lu, Lingxia; Li, Shenggang; Li, Yaping; Tao, Qian GV-like fuzzy matroids and their properties. (Chinese. English summary) Zbl 1389.05014 J. Northwest Univ., Nat. Sci. Ed. 47, No. 2, 157-161 (2017). Summary: Determination of systems of GV-like fuzzy matroid independent sets is studied by using the idea of specialization. A concrete method to induce a system of GV-like fuzzy matroid independent sets on a set \(S\) by a tower of matroids on \(S\) (resp., a system of GV-like fuzzy matroid bases on \(S\), a GV-like fuzzy rank function on \(S\)) is given. A one-to-one correspondence from \(\mathbb I(S,L)\) (the set of all systems of GV-like fuzzy matroid independent sets on \(S\)) to \(\mathbb T(S,L)\) (the set of all towers of matroids on \(S\)) or \(\mathbb B(S,L)\) (the set of all systems of GV-like fuzzy matroid bases on \(S\)), respectively is also given. MSC: 05B35 Combinatorial aspects of matroids and geometric lattices 52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) Keywords:\(L\)-matroid; tower of matroids; GV-like fuzzy matroid independent sets; GV-like fuzzy matroid bases; GV-like fuzzy rank function PDFBibTeX XMLCite \textit{S. Zhang} et al., J. Northwest Univ., Nat. Sci. Ed. 47, No. 2, 157--161 (2017; Zbl 1389.05014) Full Text: DOI