前向网络作为模糊函数泛逼近器的一致性分析

前向神经网络的泛逼近性一直是神经网络的研究热点.本文给出了连续模糊函数的定义,依Hausdorff度量,借助模糊值Bernstein多项式关于连续模糊函数的逼近性质,证明了前向网络作为模糊函数泛逼近器的一致逼近性结果,并通过实例给出了逼近性的具体实现过程.     

前向正则模糊神经网络依K-积分模的泛逼近能力

针对前向正则模糊神经网络引进K-拟可加积分和K-积分模概念,应用积分转换定理研究了该网络在K-积分模意义下对模糊值简单函数类的泛逼近能力,进而在有限K-拟可加测度空间上,借助模糊值简单函数为桥梁获得了前向正则模糊神经网络依K-积分模对(u)-可积有界模糊值函数类仍具有泛逼近性.该结果表明前向正则模糊神经网络对连续模糊系统的逼近能力可以推广为对一般可积系统的逼近能力.     

高斯型模糊前向神经网络

利用高斯型隶属函数和采样数据得到了三层模糊前向神经网络。该网络模型利用权值直接确定法得到了最优权值,并依据采样数据中的插值样本较好确定了单隐层神经元个数。该网络是近似插值神经网络。仿真实验表明,高斯型模糊前向神经网络具有逼近精度高、网络结构简单、良好的去噪性和实时性高等优点。     

一类RBF模糊神经网络的逼近性研究

本文将RBF神经网络的输入、权值以及径向基函数设为折线模糊数,构造了一类折线RBF模糊神经网络.以三角模糊数为例,讨论了折线RBF模糊神经网络的参数训练方法,通过实例验证了该网络对模糊值函数的逼近性能.     

基于三Ι算法的模糊系统及其响应性能

给出了基于三Ⅰ算法和α-三Ⅰ算法的几种典型模糊系统的插值表达式．指出,基于三Ⅰ算法和α-三Ⅰ算法的模糊系统对于某些蕴涵算子具有函数逼近的泛性,而对于不少蕴涵算子只具有阶跃输出能力,而不具有函数逼近的泛性．此外,证明了基于三Ⅰ算法的模糊系统在一定条件下对于模糊逻辑系统中推理与聚合的次序交换无关．     

插值型模糊前向神经网络

为了克服前向神经网络的固有缺陷,提出了基于采样数据建立的含单隐层神经元的模糊前向神经网络.该网络模型利用权值直接确定法得到了最优权值,网络结构可以随采样数据的多少,自主设定隐层神经元,完成了近似插值与精确插值的转换.计算机数值仿真实验表明,模糊前向神经网络具有逼近精度高、网络结构可调和实时性高的优点,并且可以实现预测和去噪.     

正则模糊神经网络在Sugeno积分模意义下的泛逼近性

首先,给出了可加模糊测度空间上Sugeno积分模的定义。然后证明了正则模糊神经网络依Sugeno积分模对模糊值函数来讲具有泛逼近性。     

基于小波神经网络的NLAR(p)过程的逼近

小波神经网络是近年来发展起来的一种逼近非线性函数的新型人工神经网络。特别是，正交尺度函数为某函数的小波神经网络更适合于函数逼近。本文在此基础上讨论了小波神经网络对非线性AR(p)过程的逼近。     

单个函数平移和伸缩的叠加在L^p（R^d）中的逼近

本文主要讨论单个函数平移和伸缩的线性组合对Ｌ＾ｐ（Ｒ＾ｎ）中一紧集内函数的逼近，给出一个很强的逼近结果，这在神经网络应用研究中具有重要意义。     

三层前馈型神经网络的最佳逼近研究

本文研究三层前馈型神经网络的最佳逼近能力,我们证明以多项式函数为隐层神经元作用函数的三层前馈型神经网络,当隐层神经元的个数超过某个给定的界限时,网络的输入输出函数张成一有限维线性空间,从而它可以实现对Ｃ（Ｋ）的最佳逼近．并且猜测,对非多项式函数的作用函数,若神经元个数有限,则它不具有最佳逼近性质．     

具有随机隐单元的渐增前馈神经网络的$L^2(R^d)$逼近能力

This paper studies approximation capability to L2(Rd) functions of incremental constructive feedforward neural networks(FNN) with random hidden units.Two kinds of therelayered feedforward neural networks are considered:radial basis function(RBF) neural networks and translation and dilation invariant(TDI) neural networks.In comparison with conventional methods that existence approach is mainly used in approximation theories for neural networks,we follow a constructive approach to prove that one may simply randomly choose parameters of hidden units and then adjust the weights between the hidden units and the output unit to make the neural network approximate any function in L2(Rd) to any accuracy.Our result shows given any non-zero activation function g :R+→R and g(x Rd) ∈ L2(Rd) for RBF hidden units,or any non-zero activation function g(x) ∈ L2(Rd) for TDI hidden units,the incremental network function fn with randomly generated hidden units converges to any target function in L2(Rd) with probability one as the number of hidden units n→∞,if one only properly adjusts the weights between the hidden units and output unit.     

多层前向正则模糊神经网络的逼近能力

Abstract. Four-layer feedforward regular fuzzy neural networks are constructed. Universal ap-proximations to some continuous fuzzy functions defined on (R)“ by the four-layer fuzzyneural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzyvalued functions are empolyed to approximate continuous fuzzy valued functions defined on eachcompact set of R“. Secondly,by introducing cut-preserving fuzzy mapping,the equivalent condi-tions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzyneural networks are shown. Finally a few of sufficient and necessary conditions for characteriz-ing approximation capabilities of regular fuzzy neural networks are obtained. And some concretefuzzy functions demonstrate our conclusions.     

Real-time stable self-learning FNN controller using genetic algorithm

A kind of real-time stable self-learning fuzzy neural network (FNN) control system is proposed in this paper. The control system is composed of two parts: (1) A FNN controller which use genetic algorithm (GA) to search optimal fuzzy rules and membership functions for the unknown controlled plant; (2) A supervisor which can guarantee the stability of the control system during the real-time learning stage, since the GA has some random property which may cause control system unstable. The approach proposed in this paper combine a priori knowledge of designer and the learning ability of FNN to achieve optimal fuzzy control for an unknown plant in real-time. The efficiency of the approach is verified by computer simulation.     

一类模糊神经网络

本文介绍了一个Ｆｕｚｚｙ神经网的三种基本形式，情况（１）是输入是实数，但权重和（或）偏差项是模糊的；情况（２）是输入是模糊的，但权重和偏差项是实数，情况（３）是输入模糊的，同时权重和（或）偏差项也是模糊的，本文集中研究情况（１），并主要讨论了情况（１）的模型性能（能力）而且得到一个较好的结果。     

神经网络的加权本质逼近阶

证明了具有单一隐层的神经网络在L_ω~q的逼近,获得了网络逼近的上界估计和下界估计.这一结果揭示了神经网络在加权逼近的意义下,网络的收敛阶与隐层单元个数之间的关系,为神经网络的应用提供了重要的理论基础.     

小卫星在轨故障诊断的模糊神经网络模型

小卫星高性能，高自主的发展趋势对于在轨故障诊断技术的实现要求日益迫切，而受小卫星体积小，重量轻，能源少的限制，当前常用的建立在高性能计算机硬件基础上的各种诊断方法不再适用于强调实时性，准确性的在轨运行监测，诊断与恢复和重构重处理。本文小卫星一体化系统总体设计技术研究与集成化设计系统为基础，采用一种神经网络与模糊系统相结合的模糊神经网络（ＦＮＮ）模型来分区域表示诊断系统并基于该ＦＮＮ模型进行诊断推量     

Triply fuzzy function approximation for hierarchical Bayesian inference

We prove that three independent fuzzy systems can uniformly approximate Bayesian posterior probability density functions by approximating the prior and likelihood probability densities as well as the hyperprior probability densities that underly the priors. This triply fuzzy function approximation extends the recent theorem for uniformly approximating the posterior density by approximating just the prior and likelihood densities. This approximation allows users to state priors and hyper-priors in words or rules as well as to adapt them from sample data. A fuzzy system with just two rules can exactly represent common closed-form probability densities so long as they are bounded. The function approximators can also be neural networks or any other type of uniform function approximator. Iterative fuzzy Bayesian inference can lead to rule explosion. We prove that conjugacy in the if-part set functions for prior, hyperprior, and likelihood fuzzy approximators reduces rule explosion. We also prove that a type of semi-conjugacy of if-part set functions for those fuzzy approximators results in fewer parameters in the fuzzy posterior approximator.     

A neural fuzzy control system with structure and parameter learning

A general connectionist model, called neural fuzzy control network (NFCN), is proposed for the realization of a fuzzy logic control system. The proposed NFCN is a feedforward multilayered network which integrates the basic elements and functions of a traditional fuzzy logic controller into a connectionist structure which has distributed learning abilities. The NFCN can be constructed from supervised training examples by machine learning techniques, and the connectionist structure can be trained to develop fuzzy logic rules and find membership functions. Associated with the NFCN is a two-phase hybrid learning algorithm which utilizes unsupervised learning schemes for structure learning and the backpropagation learning scheme for parameter learning. By combining both unsupervised and supervised learning schemes, the learning speed converges much faster than the original backpropagation algorithm. The two-phase hybrid learning algorithm requires exact supervised training data for learning. In some real-time applications, exact training data may be expensive or even impossible to obtain. To solve this problem, a reinforcement neural fuzzy control network (RNFCN) is further proposed. The RNFCN is constructed by integrating two NFCNs, one functioning as a fuzzy predictor and the other as a fuzzy controller. By combining a proposed on-line supervised structure-parameter learning technique, the temporal difference prediction method, and the stochastic exploratory algorithm, a reinforcement learning algorithm is proposed, which can construct a RNFCN automatically and dynamically through a reward-penalty signal (i.e., “good” or “bad” signal). Two examples are presented to illustrate the performance and applicability of the proposed models and learning algorithms.     

模糊神经网络方法在定点定量降水预报中的应用研究

以单站24小时降水量作为预报对象,采用模糊神经网络方法进行了新的数值预报产品释用预报方法研究.首先通过对T 213、ECMW F预报因子场以及高空气象探测资料进行处理,有效浓缩多种物理量因子场的实况及预报信息,并进一步建立了南宁、桂林、河池、百色4站的降水模糊神经网络释用预报模型.运用与实际业务相同的预报方法对2006年6—8月进行逐日的降水量预报试验,并与相同时次的T 213降水预报产品进行对比分析.结果表明,4个单站的定点、定量模糊神经网络降水预报模型,在预报性能上明显优于同期T 213数值预报模式的降水预报结果.