Characterization of \(L\)-fuzzifying matroids by \(L\)-fuzzifying closure operators. (English) Zbl 1214.05006

Summary: An \(L\)-fuzzifying matroid is a pair \((E,{\mathcal I})\), where \({\mathcal I}\) is a map from \(2^E\) to \(L\) satisfying three axioms. In this paper, the notion of closure operators in matroid theory is generalized to an \(L\)-fuzzy setting and called \(L\)-fuzzifying closure operators. It is proved that there exists a one-to-one correspondence between \(L\)-fuzzifying matroids and their \(L\)-fuzzifying closure operators.


05B35 Combinatorial aspects of matroids and geometric lattices