| 以正规多项式为基函数的标准模糊系统逼近误差公式证明 |
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| 引用本文： | 陈刚.以正规多项式为基函数的标准模糊系统逼近误差公式证明[J].大连海事大学学报(自然科学版),2007,33(2):110-115. |
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| 作者姓名： | 陈刚 |
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| 作者单位： | 大连海事大学数学系 辽宁大连116026，大连理工大学工业装备结构分析国家重点实验室，辽宁大连116024 |
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| 基金项目： | 中国博士后科学基金
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辽宁省自然科学基金 |
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| 摘 要： | 为提高模糊系统的逼近精度及扩大基函数的选择范围,定义了论域的正规二次多项式模糊划分.在标准模糊系统的基础上,提出以正规二次多项式为基函数的一类模糊系统;通过采用数值分析中的余项与辅助函数方法,对该类模糊系统进行了逼近误差精度的理论分析,给出了从SISO到MISO的一阶和准二阶误差逼近精度公式;指出该系统逼近精度公式使用的约束条件及应注意的问题.
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| 关 键 词： | 标准模糊系统 逼近误差公式 正规二次多项式模糊划分 模糊基函数 |
| 文章编号： | 1006-7736（2007）02-0110-06 |
| 修稿时间： | 2006-10-20 |
Formula proof of standard fuzzy systems with normal quartic polynomial membership functions as basic functions |
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| CHEN Gang.Formula proof of standard fuzzy systems with normal quartic polynomial membership functions as basic functions[J].Journal of Dalian Maritime University,2007,33(2):110-115. |
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| Authors: | CHEN Gang |
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| Institution: | 1. Department of Mathematics, Dalian Maritime University, Dalian 116026, China; 2. State Key Laboratory Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | The paper developed a normal quartic polynomial partition of fuzzy domain and established the standard fuzzy system with partition of normal quadratic polynomial membership functions to improve approximation precision of fuzzy system and extend the fuzzy basic functions.Based on above standard fuzzy system,approximation error formula were discussed by interpolation theory.A first order and approximative second universal approximation error bounds from SISO to MISO were given and their relations were founded.The paper employed error remainder term and auxiliary function in proving process while the used conditions and relative problems of these formula were pointed out in fuzzy systems theory and actual application. |
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| Keywords: | standard fuzzy systems approaching error formula normal quadratic polynomial fuzzy partition fuzzy basic functions |
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