摘要
给出了模糊随机集基于拟概率的分布函数、期望的定义及性质,证明了模糊随机集基于拟概率的Chebyshev不等式、Hoeffding不等式和强大数定律,提出了基于拟概率和模糊样本的经验风险泛函、期望风险泛函以及经验风险最小化原则严格一致性定义,并证明了基于拟概率和模糊样本的学习理论的关键定理。
The concepts of the distribution function and the expectation of fuzzy random sets based on Quasi-probability are given, and then Chebyshev inequality, Hoeffding inequality and the strong law of large numbers of fuzzy random sets based on Quasi-probability are proved. The expected risk funetion, the empirical risk functional and the principle of empirical risk minimization （ERM） based on Quasi-probability and fuzzy samples are presented, the key theorem of learning theory based on Quasi-probability and fuzzy samples is proved.
出处
《模糊系统与数学》
CSCD
北大核心
2016年第4期129-134,共6页
Fuzzy Systems and Mathematics
基金
河北省高等学校科学技术研究项目(Z2013038)
中国地质大学长城学院校级科研项目(ZDCYK1608)
关键词
拟概率
模糊随机集
经验风险最小化原则
关键定理
Quasi-probability
Fuzzy Random Sets
The Principle of Empirical Risk Minimization
Key Theorem
