可信性空间上基于复模糊变量的学习理论的关键定理  

The key theorem of learning theory based on complex fuzzy variable on credibility space

作　　者：田景峰[1] 张植明[2] 

机构地区：[1]华北电力大学科技学院,河北保定071051 [2]河北大学数学与计算机学院,河北保定071002

出　　处：《华北电力大学学报（自然科学版）》2009年第4期104-109,共6页Journal of North China Electric Power University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60773062);教育部科学技术研究重点资助项目(206012);河北省教育厅科研计划重点资助项目(2005001D);河北省自然科学基金资助项目(2008000633)

摘　　要：给出了可信性测度空间上复模糊变量定义及一些性质;给出了复模糊变量的经验风险泛函、期望风险泛函以及经验风险最小化原则严格一致收敛的定义。在此基础上给出并证明了基于复模糊变量的学习理论的关键定理,为系统建立可信性空间上的复统计学习理论奠定了理论基础。The definition of complex fuzzy variable is introduced, and some properties are presented on Credibility measure space. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of empirical risk minimization principle on Credibility measure space are proposed. According to these properties and concepts, the key theorem of learning theory based on complex fuzzy variable is given and proven. The investigations lay essential theoretical foundations for the systematic and comprehensive development of the complex statistical learning theory on Credibility space.

关 键 词：可信性测度空间 复模糊变量 关键定理 复统计学习理论 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O234[自动化与计算机技术—控制科学与工程]