重心法模糊系统及其概率表示  

Center-of-gravity fuzzy system and its probability representation theory

作　　者：袁学海[1] 鹿文慧[1] 李洪兴[1] 

机构地区：[1]大连理工大学电子信息与电气工程学部,辽宁大连116024

出　　处：《辽宁工程技术大学学报（自然科学版）》2010年第5期795-798,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(60774049);国家自然科学基金重大研究计划(90818025)

摘　　要：为了研究基于模糊蕴涵算子θ(a,b)=(2-a-b)∧1的重心法模糊系统及其概率表示,利用模糊推理构造出了基于输入-输出数据的联合概率密度函数,研究了这种概率分布的边缘分布和数字特征,导出了基于联合概率密度函数的回归函数。研究结果表明:这种回归函数实际上是基于给定模糊蕴涵算子的重心法模糊系统,证明了该模糊系统具有一阶逼近精度,从而进一步揭示了模糊系统的概率论意义。In order to investigate the center-of-gravity fuzzy system and its probability representation theory based on the fuzzy implication θ （ a ,b ） =（ 2 -a -b）∧ 1,the study constructs a joint probability density functions for binary random variable based on input-output data using fuzzy inference method. Based on the further study on the marginal density functions and numerical characteristics of the joint probability density function,the regression function corresponding to the probability distribution is derived. The final result shows that the regression function obtained in this study is the fuzzy system obtained through the defuzzifier of the center of gravity. Furthermore,the sufficient condition of universal approximation for the fuzzy system is given and the study reveals the significance of probability in a fuzzy system.

关 键 词：模糊系统 概率密度 数字特征 泛逼近性 

分 类 号：TP273.4[自动化与计算机技术—检测技术与自动化装置]