In this paper, the notions of independence spaces and matroids as special convexity spaces are generalized to fuzzy setting, which are called M-fuzzifying independence spaces and M-fuzzifying matroids, respectively. Some properties of M-fuzzifying closure operators and M-fuzzifying convex hull operators are discussed. By those properties and the notion of strong M-fuzzifying independence spaces, the relation between M-fuzzifying independence spaces and M-fuzzifying matroids is established.
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