In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievable example is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for the basis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroid is equivalent to a mapping which satisfies the basis axioms or circuit axioms.