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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”.