基于一类T-模的模糊Hopfield网络的稳定性分析

本文建立了基于一类T-模的一种动态模糊神经网络-(∨,T)Hopfield网.文章首先证明了系统本身的稳定性及系统平衡态的Lyapunov稳定性,然后建立了吸引子的一个非平凡吸引域,使系统具有良好的容错性.最后,通过例子验证了得到的结论.     

正则模糊神经网络对一类连续模糊值函数的普遍近似性

本文讨论了正则模糊神经网络于对定义于区间［０，Ｔ０］上连续可减模糊值函数的普遍近似性，在此基础上，证明了［０，Ｔ０］上取值为三角形模糊连续递增函数可用正则模糊神经网络逼近到任意精度。     

通信网络可靠性研究中的数学问题

系统介绍在通信网络可靠性研究中所要解决的几类数学问题,不仅分析所取得成果的特点及局限,而且指出了解决相应问题的新途径。     

Approximation capability of regular fuzzy neural networks to continuous fuzzy functions

The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function on R, some equivalent conditions are obtained, with which continuous fuzzy functions can be approximated to any degree of accuracy by the four-layer feedforward regular fuzzy neural networks.Finally a few examples of such fuzzy functions are given.     

Approximation of generalized fuzzy system to integrable function

A generalized fuzzy system by which many fuzzy models in application are extended is defined. By the approximation of the generalized Takagi-Sugeno(T-S) system to the piecewise linear function with Lp(μ)-norm, it is shown that the generalized T-S system is the universal approximator to p-integrable functions. With the given degree of accuracy, the fuzzy rule number needed in the fuzzy rule base of the system is estimated. Finally some simulation examples are given to demonstrate the conclusions.     

Image restoration techniques based on fuzzy neural networks

By establishing some suitable partitions of input and output spaces, a novel fuzzy neural network (FNN) which is called selection type FNN is developed. Such a system is a multilayer feedforward neural network, which can be a universal approximator with maximum norm. Based on a family of fuzzy inference rules that are of real senses, a simple and useful inference type FNN is constructed. As a result, the fusion of selection type FNN and inference type FNN results in a novel filter-FNN filter. It is simple in structure. And also it is convenient to design the learning algorithm for structural parameters. Further, FNN filter can efficiently suppress impulse noise superimposed on image and preserve fine image structure, simultaneously. Some examples are simulated to confirm the advantages of FNN filter over other filters, such as median filter and adaptive weighted fuzzy mean (AWFM) filter and so on, in suppression of noises and preservation of image structure.     

A novel fuzzy neural network and its approximation capability

The polygonal fuzzy numbers are employed to define a new fuzzy arithmetic. A novel ex-tension principle is also introduced for the increasing function σ:R→R. Thus it is convenient to con-struct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to the continuously increasing fuzzy functions.     

试验函数空间中的非标准分析

用非标准分析方法来研究试验函数空间E(R^n)与D(R^n)上的拓扑．对其中的单子进行了刻划．得到了这两个空间中有界性，紧性等拓扑性质的非标准特征．并十分简洁地证明了几个标准结果．最后，用非标准方法得到了E(R^n)在D′(R^n)中稠密．D(R^N)在E′(R^n)中稠密的结论.