COMPRESSION AND EXPANSION OF FUZZY RULE BASES BY USING CRISP-FUZZY NEURAL NETWORKS

A fuzzy neural network with knowledge discovery FNNKD is designed to perform adaptive compensatory fuzzy reasoning based on more useful and more heuristic primary fuzzy sets. In order to overcome the weakness of the conventional crisp neural network and the fuzzy operation oriented neural network, we have developed a general fuzzy reasoning oriented fuzzy neural network called a crisp-fuzzy neural network CFNN that is capable of extracting high-level knowledge such as fuzzy IF-THEN rules from either crisp data or fuzzy data. A CFNN can effectively compress a 5 5 fuzzy IF-THEN rule base of a cart-pole balancing system to a 3 3 one, then to a 2 2 one, and finally to a 1 1 one, and can expand on invalid sparse 3 3 fuzzy IF-THEN rule base of a cart-pole balancing system to a valid 5 5 one. In addition, a CFNN can control a more complex cart-pole balancing system with random fuzzy noise inputs and outputs i.e., nonconventional using crisp inputs and outputs without any noise . The simulations have indicated that a CFNN is an efficient neurofuzzy system with abilities to discover new fuzzy knowledge from either numerical data or fuzzy data, compress and expand fuzzy knowledge, and do fuzzy reasoning.     

Fuzzy perceptron neural networks for classifiers with numericaldata and linguistic rules as inputs

This paper presents a novel learning algorithm of fuzzy perceptron neural networks (FPNNs) for classifiers that utilize expert knowledge represented by fuzzy IF-THEN rules as well as numerical data as inputs. The conventional linear perceptron network is extended to a second-order one, which is much more flexible for defining a discriminant function. In order to handle fuzzy numbers in neural networks, level sets of fuzzy input vectors are incorporated into perceptron neural learning. At different levels of the input fuzzy numbers, updating the weight vector depends on the minimum of the output of the fuzzy perceptron neural network and the corresponding nonfuzzy target output that indicates the correct class of the fuzzy input vector. This minimum is computed efficiently by employing the modified vertex method. Moreover, the fuzzy pocket algorithm is introduced into our fuzzy perceptron learning scheme to solve the nonseparable problems. Simulation results demonstrate the effectiveness of the proposed FPNN model     

Solving fully fuzzy polynomials using feed-back neural networks

Recently, there has been a considerable amount of interest and practice in solving many problems of several applied fields by fuzzy polynomials. In this paper, we have designed an artificial fuzzified feed-back neural network. With this design, we are able to find a solution of fully fuzzy polynomial with degree n. This neural network can get a fuzzy vector as an input, and calculates its corresponding fuzzy output. It is clear that the input–output relation for each unit of fuzzy neural network is defined by the extension principle of Zadeh. In this work, a cost function is also defined for the level sets of fuzzy output and fuzzy target. Next a learning algorithm based on the gradient descent method will be defined that can adjust the fuzzy connection weights. Finally, our approach is illustrated by computer simulations on numerical examples. It is worthwhile to mention that application of this method in fluid mechanics has been shown by an example.     

General fuzzy min-max neural network for clustering andclassification

This paper describes a general fuzzy min-max (GFMM) neural network which is a generalization and extension of the fuzzy min-max clustering and classification algorithms of Simpson (1992, 1993). The GFMM method combines supervised and unsupervised learning in a single training algorithm. The fusion of clustering and classification resulted in an algorithm that can be used as pure clustering, pure classification, or hybrid clustering classification. It exhibits a property of finding decision boundaries between classes while clustering patterns that cannot be said to belong to any of existing classes. Similarly to the original algorithms, the hyperbox fuzzy sets are used as a representation of clusters and classes. Learning is usually completed in a few passes and consists of placing and adjusting the hyperboxes in the pattern space; this is an expansion-contraction process. The classification results can be crisp or fuzzy. New data can be included without the need for retraining. While retaining all the interesting features of the original algorithms, a number of modifications to their definition have been made in order to accommodate fuzzy input patterns in the form of lower and upper bounds, combine the supervised and unsupervised learning, and improve the effectiveness of operations. A detailed account of the GFMM neural network, its comparison with the Simpson's fuzzy min-max neural networks, a set of examples, and an application to the leakage detection and identification in water distribution systems are given     

Genetic algorithm-based optimal fuzzy controller design in the linguistic space

In this paper, a genetic algorithm (GA) based optimal fuzzy controller design is proposed. The design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule. The inputs of the controller, after scaling, are utilized by the index function for computing the output linguistic value. This linguistic value can then be used to map the suitable fuzzy control actions. This proposed novel fuzzy control rule has crisp input and fuzzified output characteristics. The index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables. Two types of index functions, both linear and nonlinear, are introduced for controlling systems with different degrees of nonlinearity. The parameters of the index function are obtained by applying a simple GA with a suitable fitness function. Various controlled systems result in various parameter sets depending on their dynamics. Under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions. Several simulation examples are given to verify the performance of the proposed GA-based fuzzy controller.     

Falcon: neural fuzzy control and decision systems using FKP and PFKP clustering algorithms.

Neural fuzzy networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. Examples are the Falcon-ART, and the POPFNN family of networks. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. This correspondence proposes two new networks: Falcon-FKP and Falcon-PFKP. They are extensions of the Falcon-ART network, and aimed to overcome the shortcomings faced by the Falcon-ART network itself, i.e., poor classification ability when the classes of input data are very similar to each other, termination of training cycle depends heavily on a preset error parameter, the fuzzy rule base of the Falcon-ART network may not be consistent Nauck, there is no control over the number of fuzzy rules generated, and learning efficiency may deteriorate by using complementarily coded training data. These deficiencies are essentially inherent to the fuzzy ART, clustering technique employed by the Falcon-ART network. Hence, two clustering techniques--Fuzzy Kohonen Partitioning (FKP) and its pseudo variant PFKP, are synthesized with the basic Falcon structure to compute the fuzzy sets and to automatically derive the fuzzy rules from the training data. The resultant neural fuzzy networks are Falcon-FKP and Falcon-PFKP, respectively. These two proposed networks have a lean and efficient training algorithm and consistent fuzzy rule bases. Extensive simulations are conducted using the two networks and their performances are encouraging when benchmarked against other neural and neural fuzzy systems.     

Learning control using fuzzified self-organizing radial basisfunction network

This note describes an approach to integrating fuzzy reasoning systems with radial basis function (RBF) networks and shows how the integrated network can be employed as a multivariable self-organizing and self-learning fuzzy controller. In particular, by drawing some equivalence between a simplified fuzzy control algorithm (SFCA) and a RBF network, we conclude that the RBF network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks, referred to as FBFN, with a variety of basis functions (not necessarily globally radial) synthesized from each dimension by fuzzy logical operators. On the other hand, as a result of natural generalization from RBF to SFCA, we claim that the fuzzy system like RBF is capable of universal approximation. Next, the FBFN is used as a multivariable rule-based controller but with an assumption that no rule-base exists, leading to a challenging problem of how to construct such a rule-base directly from the control environment. We propose a simple and systematic approach to performing this task by using a fuzzified competitive self-organizing scheme and incorporating an iterative learning control algorithm into the system. We have applied the approach to a problem of multivariable blood pressure control with a FBFN-based controller having six inputs and two outputs, representing a complicated control structure     

An effective neural network and fuzzy time series-based hybridized model to handle forecasting problems of two factors

Fuzzy time series forecasting method has been applied in several domains, such as stock market price, temperature, sales, crop production and academic enrollments. In this paper, we introduce a model to deal with forecasting problems of two factors. The proposed model is designed using fuzzy time series and artificial neural network. In a fuzzy time series forecasting model, the length of intervals in the universe of discourse always affects the results of forecasting. Therefore, an artificial neural network- based technique is employed for determining the intervals of the historical time series data sets by clustering them into different groups. The historical time series data sets are then fuzzified, and the high-order fuzzy logical relationships are established among fuzzified values based on fuzzy time series method. The paper also introduces some rules for interval weighing to defuzzify the fuzzified time series data sets. From experimental results, it is observed that the proposed model exhibits higher accuracy than those of existing two-factors fuzzy time series models.     

Comparison of crisp and fuzzy character neural networks inhandwritten word recognition

Experiments comparing neural networks trained with crisp and fuzzy desired outputs are described. A handwritten word recognition algorithm using the neural networks for character level confidence assignment was tested on images of words taken from the United States Postal Service mailstream. The fuzzy outputs were defined using a fuzzy k-nearest neighbor algorithm. The crisp networks slightly outperformed the fuzzy networks at the character level but the fuzzy networks outperformed the crisp networks at the word level. This empirical result is interpreted as an example of the principle of least commitment     

An improved fuzzy neural network based on T–S model

An improved fuzzy neural network based on Takagi–Sugeno (T–S) model is proposed in this paper. According to characteristics of samples spatial distribution the number of linguistic values of every input and the means and deviations of corresponding membership functions are determined. So the reasonable fuzzy space partition is got. Further a subtractive clustering algorithm is used to derive cluster centers from samples. With the parameters of linguistic values the cluster centers are fuzzified to get a more concise rule set with importance for every rule. Thus redundant rules in the fuzzy space are deleted. Then antecedent parts of all rules determine how a fuzzification layer and an inference layer connect. Next, weights of the defuzzification layer are initialized by a least square algorithm. After the network is built, a hybrid method combining a gradient descent algorithm and a least square algorithm is applied to tune the parameters in it. Simultaneous, an adaptive learning rate which is identified from input-state stability theory is adopted to insure stability of the network. The improved T–S fuzzy neural network (ITSFNN) has a compact structure, high training speed, good simulation precision, and generalization ability. To evaluate the performance of the ITSFNN, we experiment with two nonlinear examples. A comparative analysis reveals the proposed T–S fuzzy neural network exhibits a higher accuracy and better generalization ability than ordinary T–S fuzzy neural network. Finally, it is applied to predict markup percent of the construction bidding system and has a better prediction capability in comparison to some previous models.     

Inversion of neural networks by gradient descent

Inversion answers the question of which input patterns to a trained multilayer neural network approximate a given output target. This method is a tool for visualization of the information processing capability of a network stored in its weights. This knowledge about the network enables one to make informed decisions on the improvement of the training task and the choice of training sets.

An inversion algorithm for multilayer perceptrons is derived from the backpropagation scheme. We apply inversion to networks for digit recognition. We observe that the multilayer perceptrons perform well with respect to generalization, i.e. correct classification of untrained digits. They are however bad on rejection of counterexamples, i.e. random patterns. Inversion gives an explanation for this drawback. We suggest an improved training scheme, and we show that a tradeoff exists between generalization and rejection of counterexamples.     

模糊神经网络语音数据融合算法的研究

针对高嗓音环境中的语音识别问题，提出一种利用模糊神经网络进行语音数据融合的新算法。该算法按一定模糊规则对语音信号的特征参数进行模糊化，并通过神经网络对每个传感器语音信号的模糊特征参数进行分类和融合。仿真实验表明，该算法鲁棒性更强；与单传感器算法相比，语音识别率得到较大的提高。     

用B样条神经网络设计自适应模糊控制器*

本文提出一种可用于设计自适应模糊控制器的模化Ｂ样条神经网络，并给出了合适的训练算法。由于这种网络在每次训练时仅需对少量权重进行调整，因此构成的模糊控制器学习速率快，可应用于过程控制中。本文最后以电厂中过热汽温的控制为例，说明本文的设计方法是有效的。     

一种基于模糊神经网络的模拟电路故障诊断方法

提出了一种采用小波分析与遗传算法相结合的模糊神经网络对模拟电路进行故障诊断的新方法。该方法采用基于小波分析的主成分分析方法对网络的训练样本进行预处理,提取优化向量后利用遗传算法对模糊神经网络进行训练。对两个模拟电路的诊断实例表明该方法故障覆盖率高,并能有效诊断出同类方法误诊的故障类型。     

一种集成遗传算法与模糊推理的粗糙集数据分析算法

粗糙集数据分析的主要优点在于它不要求任何关于被处理数据的先验或额外的知识,文章利用其对数据库进行分析计算,自动获取数据库在各个层次上的规则集。在保证量化后的数据库具有最大一致性的前提下,利用遗传算法求取连续属性值的最优量化区间个数及各个区间分点值。同时将量化区间进行模糊化,将清晰规则集转化为模糊规则集,利用模糊推理进行决策以提高鲁棒性。通过对UCI中几个数据库的测试验证了所提出算法的有效性。     

Extracting rules from a (fuzzy/crisp) recurrent neural network using a self‐organizing map

Although the extraction of symbolic knowledge from trained feedforward neural networks has been widely studied, research in recurrent neural networks (RNN) has been more neglected, even though it performs better in areas such as control, speech recognition, time series prediction, etc. Nowadays, a subject of particular interest is (crisp/fuzzy) grammatical inference, in which the application of these neural networks has proven to be suitable. In this paper, we present a method using a self‐organizing map (SOM) for extracting knowledge from a recurrent neural network able to infer a (crisp/fuzzy) regular language. Identification of this language is done only from a (crisp/fuzzy) example set of the language. © 2000 John Wiley & Sons, Inc.     

基于模糊控制律的遗传神经匝道协调控制

讨论了快速路匝道系统中智能控制技术问题。针对匝道系统特点,分析了模糊控制、人工神经网络、遗传算法的适用性,提出了一种基于模糊控制律的遗传神经匝道协调控制方案。在该方案中,对模糊控制输入输出数据进行线性修正,使用修正后的数据完成遗传神经网络训练,并用神经网络代替模糊控制器对匝道系统进行控制。给出了神经网络结构和遗传算法流程,并结合宏观交通流模型进行系统仿真。仿真结果表明,与模糊控制相比,控制效果显著提高。     

Recurrent neural networks and robust time series prediction

We propose a robust learning algorithm and apply it to recurrent neural networks. This algorithm is based on filtering outliers from the data and then estimating parameters from the filtered data. The filtering removes outliers from both the target function and the inputs of the neural network. The filtering is soft in that some outliers are neither completely rejected nor accepted. To show the need for robust recurrent networks, we compare the predictive ability of least squares estimated recurrent networks on synthetic data and on the Puget Power Electric Demand time series. These investigations result in a class of recurrent neural networks, NARMA(p,q), which show advantages over feedforward neural networks for time series with a moving average component. Conventional least squares methods of fitting NARMA(p,q) neural network models are shown to suffer a lack of robustness towards outliers. This sensitivity to outliers is demonstrated on both the synthetic and real data sets. Filtering the Puget Power Electric Demand time series is shown to automatically remove the outliers due to holidays. Neural networks trained on filtered data are then shown to give better predictions than neural networks trained on unfiltered time series.     

Fuzzy ARTMAP: A neural network architecture for incrementalsupervised learning of analog multidimensional maps

A neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors, which may represent fuzzy or crisp sets of features. The architecture, called fuzzy ARTMAP, achieves a synthesis of fuzzy logic and adaptive resonance theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Four classes of simulation illustrated fuzzy ARTMAP performance in relation to benchmark backpropagation and generic algorithm systems. These simulations include finding points inside versus outside a circle, learning to tell two spirals apart, incremental approximation of a piecewise-continuous function, and a letter recognition database. The fuzzy ARTMAP system is also compared with Salzberg's NGE systems and with Simpson's FMMC system.     

Advanced self-organizing polynomial neural network

In this paper, we introduce a concept of advanced self-organizing polynomial neural network (Adv_SOPNN). The SOPNN is a flexible neural architecture whose structure is developed through a modeling process. But the SOPNN has a fatal drawback; it cannot be constructed for nonlinear systems with few input variables. To relax this limitation of the conventional SOPNN, we combine a fuzzy system and neural networks with the SOPNN. Input variables are partitioned into several subspaces by the fuzzy system or neural network, and these subspaces are utilized as new input variables to the SOPNN architecture. Two types of the advanced SOPNN are obtained by combining not only the fuzzy rules of a fuzzy system with SOPNN but also the nodes in a hidden layer of neural networks with SOPNN into one methodology. The proposed method is applied to the nonlinear system with two inputs, which cannot be identified by conventional SOPNN to show the performance of the advanced SOPNN. The results show that the proposed method is efficient for systems with limited data set and a few input variables and much more accurate than other modeling methods with respect to identification error.