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Fuzzy matroids and a greedy algorithm. (English) Zbl 0736.05023
A greedy algorithm for fuzzy matroids is developed. Eight definitions establish the main properties (hereditary and exchange) and some key concepts (rank function, independence, fundamental sequence, \(r\)-level matroid, etc.) for crisp and fuzzy matroids. An example illustrates the roles of them. The main results are fixed in two theorems and a lemma. The proposed greedy algorithm is effective under certain hypothesis. A basis of a matroid can be obtained for a weight function and a fuzzy set. The algorithm is briefly described as the “greediest of the greedy algorithms with respect to degree membership”.
Reviewer: C.N.Bouza (Vedado)

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
05B99 Designs and configurations
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References:
[1] Bryant, V.; Perfect, M., Independence Theory in Combinatorics (1980), Chapman and Hall: Chapman and Hall London-New York
[2] Goetschel, R.; Voxman, W., Fuzzy matroids, Fuzzy Sets and Systems, 27, 291-302 (1988) · Zbl 0651.05024
[3] Goetschel, R.; Voxman, W., Bases of fuzzy matroids, Fuzzy Sets and Systems, 31, 253-261 (1989) · Zbl 0686.05013
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