DCT-Yager FNN: a novel Yager-based fuzzy neural network with the discrete clustering technique.

Earlier clustering techniques such as the modified learning vector quantization (MLVQ) and the fuzzy Kohonen partitioning (FKP) techniques have focused on the derivation of a certain set of parameters so as to define the fuzzy sets in terms of an algebraic function. The fuzzy membership functions thus generated are uniform, normal, and convex. Since any irregular training data is clustered into uniform fuzzy sets (Gaussian, triangular, or trapezoidal), the clustering may not be exact and some amount of information may be lost. In this paper, two clustering techniques using a Kohonen-like self-organizing neural network architecture, namely, the unsupervised discrete clustering technique (UDCT) and the supervised discrete clustering technique (SDCT), are proposed. The UDCT and SDCT algorithms reduce this data loss by introducing nonuniform, normal fuzzy sets that are not necessarily convex. The training data range is divided into discrete points at equal intervals, and the membership value corresponding to each discrete point is generated. Hence, the fuzzy sets obtained contain pairs of values, each pair corresponding to a discrete point and its membership grade. Thus, it can be argued that fuzzy membership functions generated using this kind of a discrete methodology provide a more accurate representation of the actual input data. This fact has been demonstrated by comparing the membership functions generated by the UDCT and SDCT algorithms against those generated by the MLVQ, FKP, and pseudofuzzy Kohonen partitioning (PFKP) algorithms. In addition to these clustering techniques, a novel pattern classifying network called the Yager fuzzy neural network (FNN) is proposed in this paper. This network corresponds completely to the Yager inference rule and exhibits remarkable generalization abilities. A modified version of the pseudo-outer product (POP)-Yager FNN called the modified Yager FNN is introduced that eliminates the drawbacks of the earlier network and yi- elds superior performance. Extensive experiments have been conducted to test the effectiveness of these two networks, using various clustering algorithms. It follows that the SDCT and UDCT clustering algorithms are particularly suited to networks based on the Yager inference rule.     

RSPOP: rough set-based pseudo outer-product fuzzy rule identification algorithm

System modeling with neuro-fuzzy systems involves two contradictory requirements: interpretability verses accuracy. The pseudo outer-product (POP) rule identification algorithm used in the family of pseudo outer-product-based fuzzy neural networks (POPFNN) suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high-dimensional data. This decreases the interpretability of the POPFNN in linguistic fuzzy modeling. This article proposes a novel rough set-based pseudo outer-product (RSPOP) algorithm that integrates the sound concept of knowledge reduction from rough set theory with the POP algorithm. The proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes. As many possible reducts exist in a given rule set, an objective measure is developed for POPFNN to correctly identify the reducts that improve the inferred consequence. Experimental results are presented using published data sets and real-world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the POPFNN using compositional rule of inference and singleton fuzzifier (POPFNN-CRI(S)) architecture. Results showed that the proposed rough set-based pseudo outer-product algorithm reduces computational complexity, improves the interpretability of neuro-fuzzy systems by identifying significantly fewer fuzzy rules, and improves the accuracy of the POPFNN.     

Stock Trading Using RSPOP: A Novel Rough Set-Based Neuro-Fuzzy Approach

This paper investigates the method of forecasting stock price difference on artificially generated price series data using neuro-fuzzy systems and neural networks. As trading profits is more important to an investor than statistical performance, this paper proposes a novel rough set-based neuro-fuzzy stock trading decision model called stock trading using rough set-based pseudo outer-product (RSPOP) which synergizes the price difference forecast method with a forecast bottleneck free trading decision model. The proposed stock trading with forecast model uses the pseudo outer-product based fuzzy neural network using the compositional rule of inference [POPFNN-CRI(S)] with fuzzy rules identified using the RSPOP algorithm as the underlying predictor model and simple moving average trading rules in the stock trading decision model. Experimental results using the proposed stock trading with RSPOP forecast model on real world stock market data are presented. Trading profits in terms of portfolio end values obtained are benchmarked against stock trading with dynamic evolving neural-fuzzy inference system (DENFIS) forecast model, the stock trading without forecast model and the stock trading with ideal forecast model. Experimental results showed that the proposed model identified rules with greater interpretability and yielded significantly higher profits than the stock trading with DENFIS forecast model and the stock trading without forecast model.     

Fuzzy classifications using fuzzy inference networks

In this paper, fuzzy inference models for pattern classifications have been developed and fuzzy inference networks based on these models are proposed. Most of the existing fuzzy rule-based systems have difficulties in deriving inference rules and membership functions directly from training data. Rules and membership functions are obtained from experts. Some approaches use backpropagation (BP) type learning algorithms to learn the parameters of membership functions from training data. However, BP algorithms take a long time to converge and they require an advanced setting of the number of inference rules. The work to determine the number of inference rules demands lots of experiences from the designer. In this paper, self-organizing learning algorithms are proposed for the fuzzy inference networks. In the proposed learning algorithms, the number of inference rules and the membership functions in the inference rules will be automatically determined during the training procedure. The learning speed is fast. The proposed fuzzy inference network (FIN) classifiers possess both the structure and the learning ability of neural networks, and the fuzzy classification ability of fuzzy algorithms. Simulation results on fuzzy classification of two-dimensional data are presented and compared with those of the fuzzy ARTMAP. The proposed fuzzy inference networks perform better than the fuzzy ARTMAP and need less training samples.     

Support-vector-based fuzzy neural network for pattern classification

Fuzzy neural networks (FNNs) for pattern classification usually use the backpropagation or C-cluster type learning algorithms to learn the parameters of the fuzzy rules and membership functions from the training data. However, such kinds of learning algorithms usually cannot minimize the empirical risk (training error) and expected risk (testing error) simultaneously, and thus cannot reach a good classification performance in the testing phase. To tackle this drawback, a support-vector-based fuzzy neural network (SVFNN) is proposed for pattern classification in this paper. The SVFNN combines the superior classification power of support vector machine (SVM) in high dimensional data spaces and the efficient human-like reasoning of FNN in handling uncertainty information. A learning algorithm consisting of three learning phases is developed to construct the SVFNN and train its parameters. In the first phase, the fuzzy rules and membership functions are automatically determined by the clustering principle. In the second phase, the parameters of FNN are calculated by the SVM with the proposed adaptive fuzzy kernel function. In the third phase, the relevant fuzzy rules are selected by the proposed reducing fuzzy rule method. To investigate the effectiveness of the proposed SVFNN classification, it is applied to the Iris, Vehicle, Dna, Satimage, Ijcnn1 datasets from the UCI Repository, Statlog collection and IJCNN challenge 2001, respectively. Experimental results show that the proposed SVFNN for pattern classification can achieve good classification performance with drastically reduced number of fuzzy kernel functions.     

Adaptive-tree-structure-based fuzzy inference system

A new fuzzy inference system named adaptive-tree-structure-based fuzzy inference system (ATSFIS) is proposed, which is abbreviated as fuzzy tree (FT). The fuzzy partition of input data set and the membership function of every subset are obtained by means of the fuzzy binary tree structure based algorithm. Two structures of FT, FT-I, and FT-II, are presented. The characteristics of FT are: 1) The parameters of antecedent and consequent for a Takagi-Sugeno fuzzy model are learned simultaneously; and 2) The fuzzy partition of input data set is adaptive to the pattern of data distribution to optimize the number of the subsets automatically. The main advantage of FT is more suitable to solve the problems, for which the number of input dimension is large, since by using the fuzzy binary tree, every farther set will be partitioned into only two subsets no matter how large the input dimension is. Therefore, in some sense the "rule explosion" will be avoided possibly. In comparison with some existing fuzzy inference systems, it is shown that the FT is also of less computation and high accuracy. The advantages of FT are illustrated by simulation results.     

一种模糊逻辑推理神经网络的结构及算法设计

建立了一种基于模糊逻辑推理的神经网络．由样本获取的初始规则确定规则层神经元个数，并确立模糊化层与规则层之间的连接．利用黄金分割法确定模糊化层隶属度函数的初始中心和宽度；根据初始规则的结论确定清晰化层的初始权值；针对网络结构提出了改进的BP算法．仿真实例表明，网络结构合理。具有较好的非线性映射能力，改进的BP算法适合于此网络，与另一种模糊神经网络相比较具有较快的训练速度和较好的泛化能力．     

A novel fuzzy logic system based on N-version programming

For the consideration of different application systems, modeling the fuzzy logic rule, and deciding the shape of membership functions are very critical issues due to they play key roles in the design of fuzzy logic control system. This paper proposes a novel design methodology of fuzzy logic control system using the neural network and fault-tolerant approaches. The connectionist architecture with the learning capability of neural network and N-version programming development of a fault-tolerant technique are implemented in the proposed fuzzy logic control system. In other words, this research involves the modeling of parameterized membership functions and the partition of fuzzy linguistic variables using neural networks trained by the unsupervised learning algorithms. Based on the self-organizing algorithm, the membership function and partition of fuzzy class are not only derived automatically, but also the preconditions of fuzzy IF-THEN rules are organized. We also provide two examples, pattern recognition and tendency prediction, to demonstrate that the proposed system has a higher computational performance and its parallel architecture supports noise-tolerant capability. This generalized scheme is very satisfactory for pattern recognition and tendency prediction problems     

A neural fuzzy system with fuzzy supervised learning

A neural fuzzy system learning with fuzzy training data (fuzzy if-then rules) is proposed in this paper. This system is able to process and learn numerical information as well as linguistic information. At first, we propose a five-layered neural network for the connectionist realization of a fuzzy inference system. The connectionist structure can house fuzzy logic rules and membership functions for fuzzy inference. We use alpha-level sets of fuzzy numbers to represent linguistic information. The inputs, outputs, and weights of the proposed network can be fuzzy numbers of any shape. Furthermore, they can be hybrid of fuzzy numbers and numerical numbers through the use of fuzzy singletons. Based on interval arithmetics, a fuzzy supervised learning algorithm is developed for the proposed system. It extends the normal supervised learning techniques to the learning problems where only linguistic teaching signals are available. The fuzzy supervised learning scheme can train the proposed system with desired fuzzy input-output pairs which are fuzzy numbers instead of the normal numerical values. With fuzzy supervised learning, the proposed system can be used for rule base concentration to reduce the number of rules in a fuzzy rule base. Simulation results are presented to illustrate the performance and applicability of the proposed system.     

Fuzzy Neural Network Models for Classification

In this paper, we combine neural networks with fuzzy logic techniques. We propose a fuzzy-neural network model for pattern recognition. The model consists of three layers. The first layer is an input layer. The second layer maps input features to the corresponding fuzzy membership values, and the third layer implements the inference engine. The learning process consists of two phases. During the first phase weights between the last two layers are updated using the gradient descent procedure, and during the second phase membership functions are updated or tuned. As an illustration the model is used to classify samples from a multispectral satellite image, a data set representing fruits, and Iris data set.     

A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines.

This paper investigates the feasibility of applying a relatively novel neural network technique, i.e., extreme learning machine (ELM), to realize a neuro-fuzzy Takagi-Sugeno-Kang (TSK) fuzzy inference system. The proposed method is an improved version of the regular neuro-fuzzy TSK fuzzy inference system. For the proposed method, first, the data that are processed are grouped by the k-means clustering method. The membership of arbitrary input for each fuzzy rule is then derived through an ELM, followed by a normalization method. At the same time, the consequent part of the fuzzy rules is obtained by multiple ELMs. At last, the approximate prediction value is determined by a weight computation scheme. For the ELM-based TSK fuzzy inference system, two extensions are also proposed to improve its accuracy. The proposed methods can avoid the curse of dimensionality that is encountered in backpropagation and hybrid adaptive neuro-fuzzy inference system (ANFIS) methods. Moreover, the proposed methods have a competitive performance in training time and accuracy compared to three ANFIS methods.     

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.     

Hybrid identification of fuzzy rule‐based models

In this study, we propose a hybrid identification algorithm for a class of fuzzy rule‐based systems. The rule‐based fuzzy modeling concerns structure optimization and parameter identification using the fuzzy inference methods and hybrid structure combined with two methods of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model concern a simplified and linear type of inference. The proposed hybrid optimal identification algorithm is carried out using a combination of genetic algorithms and an improved complex method. The genetic algorithms determine initial parameters of the membership function of the premise part of the fuzzy rules. In the sequel, the improved complex method (being in essence a powerful auto‐tuning algorithm) leads to fine‐tuning of the parameters of the respective membership functions. An aggregate performance index with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model obtained for the training and testing data. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature. © 2002 John Wiley & Sons, Inc.     

An ART-based fuzzy adaptive learning control network

This paper addresses the structure and an associated online learning algorithm of a feedforward multilayer neural net for realizing the basic elements and functions of a fuzzy controller. The proposed fuzzy adaptive learning control network (FALCON) can be contrasted with traditional fuzzy control systems in network structure and learning ability. An online structure/parameter learning algorithm, FALCON-ART, is proposed for constructing FALCON dynamically. It combines backpropagation for parameter learning and fuzzy ART for structure learning. FALCON-ART partitions the input state space and output control space using irregular fuzzy hyperboxes according to the data distribution. In many existing fuzzy or neural fuzzy control systems, the input and output spaces are always partitioned into “grids”. As the number of variables increases, the number of partitioned grids grows combinatorially. To avoid this problem in some complex systems, FALCON-ART partitions the I/O spaces flexibly based on data distribution. It can create and train FALCON in a highly autonomous way. In its initial form, there is no membership function, fuzzy partition, and fuzzy logic rule. They are created and begin to grow as the first training pattern arrives. Thus, the users need not give it any a priori knowledge or initial information. FALCON-ART can online partition the I/O spaces, tune membership functions, find proper fuzzy logic rules, and annihilate redundant rules dynamically upon receiving online data     

A fuzzy controller with supervised learning assisted reinforcement learning algorithm for obstacle avoidance

Fuzzy logic systems are promising for efficient obstacle avoidance. However, it is difficult to maintain the correctness, consistency, and completeness of a fuzzy rule base constructed and tuned by a human expert. A reinforcement learning method is capable of learning the fuzzy rules automatically. However, it incurs a heavy learning phase and may result in an insufficiently learned rule base due to the curse of dimensionality. In this paper, we propose a neural fuzzy system with mixed coarse learning and fine learning phases. In the first phase, a supervised learning method is used to determine the membership functions for input and output variables simultaneously. After sufficient training, fine learning is applied which employs reinforcement learning algorithm to fine-tune the membership functions for output variables. For sufficient learning, a new learning method using a modification of Sutton and Barto's model is proposed to strengthen the exploration. Through this two-step tuning approach, the mobile robot is able to perform collision-free navigation. To deal with the difficulty of acquiring a large amount of training data with high consistency for supervised learning, we develop a virtual environment (VE) simulator, which is able to provide desktop virtual environment (DVE) and immersive virtual environment (IVE) visualization. Through operating a mobile robot in the virtual environment (DVE/IVE) by a skilled human operator, training data are readily obtained and used to train the neural fuzzy system.     

Partitioning of feature space for pattern classification

The article proposes a simple approach for finding a fuzzy partitioning of a feature space for pattern classification problems. A feature space is initially decomposed into some overlapping hyperboxes depending on the relative positions of the pattern classes found in the training samples. A few fuzzy if-then rules reflecting the pattern classes by the generated hyperboxes are then obtained in terms of a relational matrix. The relational matrix is utilized in the modified compositional rule of inference in order to recognize an unknown pattern. The proposed system is capable of handling imprecise information both in the learning and the processing phases. The imprecise information is considered to be either incomplete or mixed or interval or linguistic in form. Ways of handling such imprecise information are also discussed. The effectiveness of the system is demonstrated on some synthetic data sets in two-dimensional feature space. The practical applicability of the system is verified on four real data such as the Iris data set, an appendicitis data set, a speech data set and a hepatic disease data set.     

Multistage fuzzy inference formulated as linguistic-truth-valuepropagation and its learning algorithm based on back-propagating errorinformation

Multistage fuzzy inference, where in the consequence in an inference stage is passed to the next stage as a fact, is studied and formulated as a type of linguistic-truth-value propagation, based on a concept of linguistic similarities between conditional propositions in successive stages. The formulation is useful in studying the characteristics of multistage fuzzy inference and reveals its structural relationship to multilayer perceptrons. The learning algorithm for multistage fuzzy inference is then derived, using backpropagating error information. The algorithm provides a means of automatically training the multistage fuzzy inference network, using input-output exemplar patterns. Intermediate membership functions based on simulation results, which are generated automatically in the intermediate stage, are proposed. The intermediate stage fuzzy-classifies the input space using intermediate membership functions. In this way, intermediate membership functions provide information regarding regional characteristics in exemplar patterns     

一种新的基于神经模糊推理网络的复杂系统模糊辨识方法

针对基于输入输出数据的复杂系统的模糊辨识问题,提出了一种新的神经模糊推理网络及相应的学习算法．学习算法被应用于系统的结构辨识与参数辨识．在结构辨识阶段,介绍了一种新的直接从输入输出数据中抽取和优化模糊规则的学习算法;在参数辨识阶段,提出和推导了一种非监督学习和监督学习相结合的混合式学习算法,实现模糊隶属函数的初步调整和优化．仿真结果表明,本文的方法可以同时满足对辨识精度、收敛速度、可读性和规则数的要求．     

Dempster–Shafer structure based fuzzy logic system for stochastic modeling

The Dempster–Shafer (D–S) theory of evidence is introduced to improve fuzzy inference under the complex stochastic environment. The Dempster–Shafer based fuzzy set (DFS) is first proposed, together with its union and intersection operations, to capture the principal stochastic uncertainties. Then, the fuzzy inference will be modified based on the extensional Dempster rule of combination. This new approach is able to capture the stochastic disturbance acting on fuzzy membership function, and provide a more effective inference under strong stochastic uncertainty. Finally, the numerical simulation and the experimental prediction of the wind speed are conducted to show the potential of the proposed method in stochastic modeling.     

A new method for constructing membership functions and fuzzy rulesfrom training examples

To extract knowledge from a set of numerical data and build up a rule-based system is an important research topic in knowledge acquisition and expert systems. In recent years, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a new fuzzy learning algorithm based on the alpha-cuts of equivalence relations and the alpha-cuts of fuzzy sets to construct the membership functions of the input variables and the output variables of fuzzy rules and to induce the fuzzy rules from the numerical training data set. Based on the proposed fuzzy learning algorithm, we also implemented a program on a Pentium PC using the MATLAB development tool to deal with the Iris data classification problem. The experimental results show that the proposed fuzzy learning algorithm has a higher average classification ratio and can generate fewer rules than the existing algorithm.