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GV-like fuzzy matroids and their properties. (Chinese. English summary) Zbl 1389.05014

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.)
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