| 可信性空间上基于复模糊变量的学习理论的关键定理 |
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| 引用本文： | 田景峰,张植明.可信性空间上基于复模糊变量的学习理论的关键定理[J].华北电力大学学报,2009,36(4). |
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| 作者姓名： | 田景峰 张植明 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目，教育部科学技术研究重点资助项目，河北省教育厅科研计划重点资助项目，河北省自然科学基金资助项目 |
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| 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。
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| 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 |
The key theorem of learning theory based on complex fuzzy variable on credibility space |
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| TIAN Jing-feng,ZHANG Zhi-ming.The key theorem of learning theory based on complex fuzzy variable on credibility space[J].Journal of North China Electric Power University,2009,36(4). |
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| Authors: | TIAN Jing-feng ZHANG Zhi-ming |
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| Affiliation: | 1.Science & Technology College North China Electric Power University;Baoding 071051;China;2.College of Mathematics and Computer Sciences;Hebei University;Baoding 071002;China |
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| Abstract: | 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... |
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| Keywords: | credibility measure space complex fuzzy variable the key theorem complex statistical learning theory |
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