Evaluation of fuzzy regression models by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate solution of fuzzy linear systems of the form Ax = Bx + d, where A and B are two square matrices of fuzzy coefficients, x and d are two fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution, a simple and fast algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

Evaluation of fully fuzzy matrix equations by fuzzy neural network

In this paper, a new hybrid method based on fuzzy neural network for approximate solution of fully fuzzy matrix equations of the form AX=D$\mathit{AX}=D$, where A and D are two fuzzy number matrices and the unknown matrix X is a fuzzy number matrix, is presented. Then, we propose some definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy matrix equations and fuzzy neural network. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of fuzzy matrix equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the fuzzy neural network is proposed. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.     

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.     

三层前向神经网络的一致逼近性

近年来，前向神经网络泛逼近的一致性分析一直为众多学者所重视。本文系统分析三层前向网络对于拟差值保序函数族的一致逼近性，其中，转换函数σ是广义Sigmoidal函数。并将此一致性结果用于建立一类新的模糊神经网络(FNN)，即折线FNN．研究这类网络对于两个给定的模糊函数的逼近性，相关结论在分析折线FNN的泛逼近性时起关键作用。     

广义Fuzzy逻辑回归模型的最大Fuzzy积分估计

以两个Fuzzy集的平均相容度为基础,给出广义Fuzzy逻辑回归模型的未知参数的最大Fuzzy积分估计,这种估计能给了近似地构造广义Fuzzy函数及求广义Fuzzy关系方程的近似解的一种简便方法。     

基于知识的模糊神经网络的旋转机械故障诊断

提出了一种基于知识的模糊神经网络并用于故障诊断．首先基于粗糙集对样本数据进行初步规则获取,并计算规则的依赖度和条件覆盖度,然后根据规则数目进行模糊神经网络结构部分设计,规则的依赖度和条件覆盖度用于设定网络初始权重,而用遗产算法对神经网络输出参数进行优化．这样的模糊神经网络称为基于知识的模糊神经网络．使用该网络对旋转机械常见故障进行诊断,结果表明,和一般模糊神经网络相比,该网络具有训练时间短而诊断率高的特点．     

An architecture of fuzzy neural networks for linguistic processing

Fuzzy sets have been used successfully in order to deal with imprecise data, linguistic terms or not well-defined concepts. Recently, considerable effort has been made in the direction of combining the neural network approach with fuzzy sets. In this paper a fuzzy feed-forward neural network, able to process trapezoidal fuzzy sets, has been investigated. Normalized trapezoidal fuzzy sets have been considered. The fuzzy generalized delta rule with different back-propagation algorithms is discussed. The more interesting and characteristic property of the proposed architecture is the ability of each node to process fuzzy sets or linguistic terms, preserving the simplicity of the back-propagation algorithm. Consequently, the resulting architecture is able to cope with problems in which the input parameters and the desired targets are described by linguistic terms. This methodology has the further interesting characteristic of being able to operate at the linguistic level rather than at the numerical level, that is it can work at a higher data abstraction level. An example in computerized electrocardiography will be illustrated in order to test the proposed approach.     

基于粒子群的模糊神经网络的短时交通流量组合预测

为了进一步提高短时交通流量预测的精度,提出了一种粒子群算法的模糊神经网络组合预测模型,模糊神经网络融合了神经网络的学习机制和模糊系统的语言推理能力等优点,弥补各自不足,将自回归求和滑动平均(ARIMA)和灰色Verhulst模型进行初步预测,并将两种初步预测的结果作为模糊神经网络的输入,构建基于改进模神经网络的组合预测模型,在此基础上进行训练和预测,其中模糊神经网络的相关参数由改进粒子群来优化,利用本方法来对南京市汉中路短时交通流量进行预测,结论表明:方法充分发挥了单一模型的优势,比单一的预测模型更加精确,是短时交通流量预测的一个有效方法。     

Ten years of genetic fuzzy systems: current framework and new trends

Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. Neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms.The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems. After a brief introduction to models and applications of genetic fuzzy systems, the field is overviewed, new trends are identified, a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated, and open questions that remain to be addressed in the future are raised. The paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems.     

An Algorithm for Solving Inverse Geoelectrics Problems Based on the Neural Network Approximation

A neural network approximation algorithm for solving inverse geoelectrics problems in the class of grid (block) models of media is presented. The algorithm is based on using neural networks for constructing an approximate inverse operator and enables formalized construction of solutions of inverse geoelectrics problem with a total number of sought-for medium parameters of ~ n · 10³. The correctness of the problem of constructing neural network inverse operators is considered. A posteriori estimates of the degree of ambiguity of solutions of the resulting inverse problem are calculated. The operation of the algorithm is illustrated by examples of 2D and 3D inversions of synthetic and field geoelectric data obtained by the MTS method.     

Analytical solution of stochastic differential equation by multilayer perceptron neural network approximation of Fokker–Planck equation

The Fokker–Planck equation is a useful tool to analyze the transient probability density function of the states of a stochastic differential equation. In this paper, a multilayer perceptron neural network is utilized to approximate the solution of the Fokker–Planck equation. To use unconstrained optimization in neural network training, a special form of the trial solution is considered to satisfy the initial and boundary conditions. The weights of the neural network are calculated by Levenberg–Marquardt training algorithm with Bayesian regularization. Three practical examples demonstrate the efficiency of the proposed method.     

An adaptive membrane algorithm for solving combinatorial optimization problems

Membrane algorithms (MAs), which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The empirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural network and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.     

AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS

Membrane algorithms （MAs）, which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

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.     

基于GA-BP的模糊神经网络控制器与Elman辨识器的系统设计

提出了一种基于神经网络的模糊控制系统 ,该系统由模糊神经网络控制器和模型辨识网络组成 .文中介绍了模糊神经网络控制器采用遗传算法离线优化与 BP算法在线调整 ,给出了具体控制算法 ,推导了变形 Elmam网络的系统辨识算法 .仿真结果表明了此法的可行性和有效性 .     

On the equivalence of neural nets and fuzzy expert systems

We show, under the assumptions described in the paper, that: (1) we can approximate a neural net to any degree of accuracy using a fuzzy expert system; and conversely (2) we may approximate a fuzzy expert system to any degree of accuracy with a neural net.     

Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms

In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction–diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits.