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We propose a fuzzy step size least-mean-square (LMS) algorithm, in which an appropriate step size is selected by a fuzzy inference system (FIS) to achieve faster convergence rate and lower steady-state fluctuation. An adaptive fuzzy sequential partial update scheme is developed to reduce system complexity without trading off bit-error rate (BER) and convergence/tracking performance. Simulations of a DS-CDMA interference suppression receiver illustrate the robust convergence and tracking behavior of the proposed LMS-based approaches with various fuzzy input vectors and fuzzy sets. The performance advantages of the proposed algorithms over other LMS algorithms in multipath Rayleigh-fading channels are investigated as well.