本文介绍双重粗糙理论的基本内容;提出双重粗糙经验风险泛函,双重粗糙期望风险泛函,双重粗糙经验风险最小化原则等概念;最后证明基于双重粗糙样本的统计学习理论的关键定理并讨论学习过程一致收敛速度的界。为系统建立基于不确定样本的统计学习理论并构建相应的支持向量机奠定了理论基础。 This paper introduces the basic content of the dual rough theory, puts forward the concepts of double rough empirical risk functional, double rough expectations risk functional, and the principle of minimizing the double rough empirical risk. Finally, we prove the key theorems of statistical learning theory based on double rough samples and discuss the learning The process of uniform convergence rate of the world. It lays a theoretical foundation for the systematic establishment of statistical learning theory based on the uncertain samples and construction of the corresponding support vector machines.