A new approach to the fuzzification of matroids

In this paper, the concept of closed fuzzy pre-matroids is generalized to L-fuzzy set theory when L is a complete lattice. It is also called an L-fuzzifying matroid. In the definition of L-fuzzifying matroids, each subset can be regarded as an independent set to some degree. When L is completely distributive, an L-fuzzifying matroid can be characterized by means of its L-fuzzifying rank function. An L-fuzzifying matroid and its L-fuzzifying rank function are one-to-one corresponding.