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Fast inference using transition matrices (FITMs) was recently presented as a new fast algorithm for performing inferences in fuzzy systems. However, this algorithm only applies to the standard additive model (SAM) using the sum-product inference composition. In this paper, we show how this methodology carries over to more general Mamdani fuzzy systems, i.e., those using t-norms and t-conorms that satisfy a requirement of distributivity. In addition, FITM, as originally described, requires inputs to be fuzzy sets. We here extend this methodology to handle crisp inputs as well.