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This paper introduces an interconnected type-1 fuzzy algorithm which is trained by a modified version of the Scaled Conjugated Gradient method for impulsive noise cancellation in discrete multitone/orthogonal frequency-division multiplexing (DMT/OFDM)-based systems for broadband power line communications. The advanced algorithm makes use of the fuzzy systems capacity of dealing with uncertainties to reduce the presence of high-power impulsive noises while the DMT/OFDM technique copes with the severe intersymbol interference observed in power line channels. As a result, for a given error probability, a high number of bits can be allotted to each subchannel due to the signal-to-noise ratio enhancements achieved by the proposed fuzzy algorithm. The simulation results show that the novel fuzzy algorithm not only achieve a high data rate, but it also outperforms the standard impulsive noises techniques and other computational intelligence-based techniques, especially in the presence of additive and high-power impulsive noises.