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中文摘要：
关键定理是统计学习理论的重要组成部分,但其研究主要集中在实随机样本且假设样本不受噪声的影响。鉴于此,提出了受噪声影响的模糊随机经验风险最小化原则的定义,给出并证明了受噪声影响的模糊随机样本的学习理论的关键定理。
英文摘要：
The key theorem plays an important role in the statistical learning theory. However, the researches mainly focus on the real random samples and the samples are supposed to be noise-free. In consideration of the facts, the definition of fuzzy random empirical risk mning theory with fuzzy random samples corrupted by noise is proposed and proved, inimization principle corrupted by noise is proposed and the key theorem of learning theory with fuzzy random samples corrupted by noise is proposed and proved.
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