研究基于输入-输出数据的重心法模糊系统及其泛逼近性。首先,将一组单输入-单输出数据转换成模糊推理规则,通过选择适当的模糊蕴涵算子生成模糊关系,再利用这种模糊关系求出二维随机变量的联合概率密度函数。当将模糊蕴涵分别取为Larsen蕴涵和Mamdani蕴涵时,分别得到了两种具体的概率密度函数(称之为Larsen分布和Mamdani分布)。其次,利用这两种概率分布,分别求出了对应的两种回归函数,指出这种回归函数实际上是模糊控制中的重心法模糊系统。我们分别给出了这种模糊系统具有泛逼近性的充分条件。从而进一步揭示了模糊系统的概率论意义。
In this paper,we study center-of gravity fuzzy systems and their universal approximations based on a set data of input-output.Firstly,a set data of input-output is transferred into fuzzy inference rules and the joint probability density functions for some binary random variable are derived by choosing fuzzy implications and building fuzzy relations.When Larsen implication and Mamdani implication are chosen,two kinds of probability density functions,which are called Larsen distribution and Mamdani distribution respectively,are obtained.Secondly,the regression functions corresponding the two probability distributions are obtained and it is shown that the regression functions obtained in this manner are the fuzzy systems obtained by defuzzifier of the center of gravity.The sufficient conditions of universal approximations for the two fuzzy systems are given.These discussions further reveal the probability consideration of fuzzy systems.