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In this paper, we analyze Xu and Yuille's robust principal component analysis (RPCA) learning algorithms by means of the distance measurement in space. Based on the analysis, a family of fuzzy RPCA learning algorithms is proposed, which is robust against outliers. These algorithms can explicitly be understood from the viewpoint of fuzzy set theory, though Xu and Yuille's algorithms were proposed based on a statistical physics approach. In the proposed algorithms, an adaptive learning procedure overcomes the difficulty of selection of learning parameters in Xu and Yuille's algorithms. Furthermore, the robustness of proposed algorithms is investigated by using the theory of influence functions. Simulations are carried out to illustrate the robustness of these algorithms.