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In this paper, a novel approach for function approximation based on robust fuzzy regression algorithm and particle swarm optimization is proposed. First, the robust fuzzy regression algorithm is applied to construct Takagi-Sugeno-Kang fuzzy model. The robust fuzzy regression algorithm is not only to simultaneously identify parameters in the premise parts and the consequent parts, but it also defines the number of fuzzy rules to fit for Takagi-Sugeno-Kang model. In addition, the robust fuzzy regression algorithm has robust learning effects when noise and outliers exist. Thereafter, particle swarm optimization is conducted to fine tune parameters from obtained fuzzy model. In simulation results, particle swarm optimization can improve Takagi-Sugeno-Kang fuzzy model built by robust fuzzy regression algorithm efficiently. The proposed approach can find best solutions when compared with other learning algorithms for four test functions.