In this paper, a new definition of M-fuzzifying derived operators on matroids is introduced and their characterizations are given. What’s more, it is shown that there is a one-to-one correspondence between M-fuzzifying matroids and M-fuzzifying derived operators, and there is also a one-to-one correspondence between M-fuzzifying closure operators and M-fuzzifying derived operators. Besides, we can obtain an M-fuzzifying closure operator induced by an M-fuzzifying matroid directly.
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