In this paper, motivated by the free product of crisp matroids, the free product of M-fuzzifying matroids is defined when M is a finite Boolean algebra and a number of fundamental properties of the operation are derived. Parallel to crisp matroids, the minors of M-fuzzifying matroids are described in terms of the M-fuzzifying truncation operator and its dual, the M-fuzzifying Higgs lift operator.
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