Support vector learning for fuzzy rule-based classification systems

To design a fuzzy rule-based classification system (fuzzy classifier) with good generalization ability in a high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, the support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high- (or even infinite) dimensional feature space. This paper investigates the connection between fuzzy classifiers and kernel machines, establishes a link between fuzzy rules and kernels, and proposes a learning algorithm for fuzzy classifiers. We first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function. Fuzzy inference on the IF-part of a fuzzy rule can be viewed as evaluating the kernel function. The kernel function is then proven to be a Mercer kernel if the reference functions meet a certain spectral requirement. The corresponding fuzzy classifier is named positive definite fuzzy classifier (PDFC). A PDFC can be built from the given training samples based on a support vector learning approach with the IF-part fuzzy rules given by the support vectors. Since the learning process minimizes an upper bound on the expected risk (expected prediction error) instead of the empirical risk (training error), the resulting PDFC usually has good generalization. Moreover, because of the sparsity properties of the SVMs, the number of fuzzy rules is irrelevant to the dimension of input space. In this sense, we avoid the "curse of dimensionality." Finally, PDFCs with different reference functions are constructed using the support vector learning approach. The performance of the PDFCs is illustrated by extensive experimental results. Comparisons with other methods are also provided.     

A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.     

Developing a new uncertain rule-based fuzzy approach for evaluating the blast-induced backbreak

This study proposes a new uncertain rule-based fuzzy approach for the evaluation of blast-induced backbreak. The proposed approach is based on rock engineering systems (RES) updated by the fuzzy system. Additionally, a genetic algorithm (GA) and imperialist competitive algorithm (ICA) were employed for the prediction aim. The most key step in modeling of fuzzy RES is the coding of the interaction matrix. This matrix is responsible for analyzing the interrelationships among the parameters influencing the rock engineering activities. The codes of the interaction matrix are not unique; thus, probabilistic coding can be done non-deterministically, which allows the uncertainties to be considered in the RES analysis. To achieve the objective of this research, 62 blasts in Shur River dam region, located in south of Iran, were investigated and the required datasets were measured. The performance of the proposed models was then evaluated in accordance with the statistical criteria such as coefficient of determination (R²). The results signify the effectiveness of the proposed GA- and ICA-based models in the simulating process. R² of 0.963 and 0.934 obtained from ICA- and GA-based models, respectively, revealed that both models were capable of predicting the backbreak. Further, the fuzzy RES was introduced as a powerful uncertain approach to evaluate and predict the backbreak.

     

基于F-SVMs的多模型建模方法

针对全局模型难以精确描述复杂工业过程的问题,提出一种基于模糊支持向量机(F-SVMs)的多模型(F-SVMs MM)建模方法。用模糊支持向量分类算法(F-SVC)对输入数据进行预处理,得到多模型模糊隶属度;用模糊支持回归算法(F-SVR)建立多模型(MM)估计器。应用该方法对pH中和滴定过程进行建模,仿真结果表明,F-SVMs MM跟踪性能好、泛化能力强,比USOCPN方法和标准支持向量机(SVMs)方法具有更好的性能和推广能力。     

A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm     

The fuzzy crystallization algorithm: a new approach to complexsystems modeling

A new identification method for fuzzy modeling is introduced. Since the method has some analogy with the process of material crystallization in nature, the name of fuzzy crystallization algorithm (FCA) is given to this novel approach. This method accomplishes structure identification and parameter identification at the same time, and possesses the properties of simplicity, flexibility, and high calculation speed. Compared with other modeling strategies, it is easier to construct a model with a specific accuracy. Numerical examples are provided to demonstrate the performance of this approach.     

A fuzzy rule-based meta-scheduler with evolutionary learning for grid computing

Grid computing is increasingly emerging as a promising platform for large-scale problems solving in science, engineering and technology. Nevertheless, a major effort is still required to harness the high potential performance of such computational framework and in this sense, an important challenge is to develop new strategies that efficiently address scheduling on the distributed, heterogeneous and shared environment of grids. Fuzzy rule-based systems (FRBSs) models are dynamic and are currently attracting the interest of scheduling research community to obtain near-optimal solutions on grids. However, FRBSs performance is strongly related to the quality of their knowledge bases and thus, with the knowledge acquisition process. Due to the inherent dynamic nature and the typical complex search spaces of grids, automatically finding a high-quality knowledge base that accurately describes the fuzzy system is extremely relevant. In this work, we propose a scheduling system for grids considering a novel learning strategy inspired by Michigan and Pittsburgh approaches that applies genetic algorithms (GAs) to evolve the fuzzy rule bases and improves the classical learning strategies in terms of computational effort and convergence behaviour. In addition, experimental results show that the proposed schema significantly outperforms other extensively used scheduling strategies.     

A new approach to fuzzy modeling and control for nonlinear dynamic systems: Neuro-fuzzy dynamic characteristic modeling and adaptive control mechanism

The study on nonlinear control system has received great interest from the international research field of automatic engineering. There are currently some alternative and complementary methods used to predict the behavior of nonlinear systems and design nonlinear control systems. Among them, characteristic modeling (CM) and fuzzy dynamic modeling are two effective methods. However, there are also some deficiencies in dealing with complex nonlinear system. In order to overcome the deficiencies, a novel intelligent modeling method is proposed by combining fuzzy dynamic modeling and characteristic modeling methods. Meanwhile, the proposed method also introduces the low-level learning power of neural network into the fuzzy logic system to implement parameters identification. This novel method is called neuro-fuzzy dynamic characteristic modeling (NFDCM). The neuro-fuzzy dynamic characteristic model based overall fuzzy control law is also discussed. Meanwhile the local adaptive controller is designed through the golden section adaptive control law and feedforward control law. In addition, the stability condition for the proposed closed-loop control system is briefly analyzed. The proposed approach has been shown to be effective via an example. Recommended by Editor Young-Hoon Joo. This work was jointly supported by National Natural Science Foundation of China under Grant 60604010, 90716021, and 90405017 and Foundation of National Laboratory of Space Intelligent Control of China under Grant SIC07010202. Xiong Luo received the Ph.D. degree from Central South University, Changsha, China, in 2004. From 2005 to 2006, he was a Postdoctoral Fellow in the Department of Computer Science and Technology at Tsinghua University. He currently works as an Associate Professor in the Department of Computer Science and Technology, University of Science and Technology Beijing. His research interests include intelligent control for spacecraft, intelligent optimization algorithms, and intelligent robot system. Zengqi Sun received the bachelor degree from Tsinghua University, Beijing, China, in 1966, and the Ph.D. degree from Chalmers University of the Technology, Gothenburg, Sweden, in 1981. He currently works as a Professor in the Department of Computer Science and Technology, Tsinghua University. His research interests include intelligent control of robotics, fuzzy neural networks, and intelligent flight control. Fuchun Sun received the Ph.D. degree from Tsinghua University, Beijing, China, in 1998. From 1998 to 2000, he was a Postdoctoral Fellow in the Department of Automation at Tsinghua University, where he is currently a Professor in the Department of Computer Science and Technology. His research interests include neural-fuzzy systems, variable structure control, networked control systems, and robotics.     

MOGUL: A methodology to obtain genetic fuzzy rule-based systems under the iterative rule learning approach

The main aim of this paper is to present MOGUL, a Methodology to Obtain Genetic fuzzy rule-based systems Under the iterative rule Learning approach. MOGUL will consist of some design guidelines that allow us to obtain different genetic fuzzy rule-based systems, i.e., evolutionary algorithm-based processes to automatically design fuzzy rule-based systems by learning and/or tuning the fuzzy rule base, following the same generic structure and able to cope with problems of a different nature. A specific evolutionary learning process obtained from the paradigm proposed to design unconstrained approximate Mamdani-type fuzzy rule-based systems will be introduced, and its accuracy in the solving of a real-world electrical engineering problem will be analyzed. ©1999 John Wiley & Sons, Inc.     

A fuzzy reasoning approach for rule-based systems based on fuzzylogics

This paper presents a weighted fuzzy reasoning algorithm for rule-based systems based on weighted fuzzy logics. The proposed algorithm allows the truth values of the conditions appearing in the antecedent portions of the rules, the certainty factors of the rules, and the weights of the conditions appearing in the antecedent portions of the rules to be represented by trapezoidal fuzzy numbers. Given the fuzzy truth values of some conditions, the algorithm can perform weighted fuzzy reasoning to evaluate the fuzzy truth values of other conditions automatically.     

An integrated approach to fuzzy learning vector quantization andfuzzy c-means clustering

Derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c-means and fuzzy learning vector quantization. These algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning. Derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent. A close relationship between the resulting algorithms and fuzzy c-means is revealed by investigating the functionals involved. It is also shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition     

Support vector machines for urban growth modeling

This paper presents a novel method to model urban land use conversion using support vector machines (SVMs), a new generation of machine learning algorithms used in the classification and regression domains. This method derives the relationship between rural-urban land use change and various factors, such as population, distance to road and facilities, and surrounding land use. Our study showed that SVMs are an effective approach to estimating the land use conversion model, owing to their ability to model non-linear relationships, good generalization performance, and achievement of a global and unique optimum. The rural-urban land use conversions of New Castle County, Delaware between 1984–1992, 1992–1997, and 1997–2002 were used as a case study to demonstrate the applicability of SVMs to urban expansion modeling. The performance of SVMs was also compared with a commonly used binomial logistic regression (BLR) model, and the results, in terms of the overall modeling accuracy and McNamara’s test, consistently corroborated the better performance of SVMs.     

A parsimony fuzzy rule-based classifier using axiomatic fuzzy set theory and support vector machines

This paper proposes a classification method that is based on easily interpretable fuzzy rules and fully capitalizes on the two key technologies, namely pruning the outliers in the training data by SVMs (support vector machines), i.e., eliminating the influence of outliers on the learning process; finding a fuzzy set with sound linguistic interpretation to describe each class based on AFS (axiomatic fuzzy set) theory. Compared with other fuzzy rule-based methods, the proposed models are usually more compact and easily understandable for the users since each class is described by much fewer rules. The proposed method also comes with two other advantages, namely, each rule obtained from the proposed algorithm is simply a conjunction of some linguistic terms, there are no parameters that are required to be tuned. The proposed classification method is compared with the previously published fuzzy rule-based classifiers by testing them on 16 UCI data sets. The results show that the fuzzy rule-based classifier presented in this paper, offers a compact, understandable and accurate classification scheme. A balance is achieved between the interpretability and the accuracy.     

Fuzzy CoCo: a cooperative-coevolutionary approach to fuzzy modeling

Co-evolutionary algorithms have received increased attention in the past few years within the domain of evolutionary computation. In this paper, we combine the search power of co-evolutionary computation with the expressive power of fuzzy systems, and introduce a novel algorithm, called Fuzzy CoCo (fuzzy cooperative coevolution). We demonstrate the efficacy of Fuzzy CoCo by applying it to a hard, real-world problem - breast cancer diagnosis, obtaining the best results to date while expending less computational effort than previous processes. Analyzing our results, we derive guidelines for setting the algorithm parameters given a (hard) problem to solve. We hope Fuzzy CoCo proves to be a powerful tool in the fuzzy modeler toolkit     

A new scheme for fuzzy rule-based system identification and itsapplication to self-tuning fuzzy controllers

There are many important issues that need to be resolved for identification of a fuzzy rule-based system using clustering. We address three such important issues: 1) deciding on the proper domain(s) of clustering; 2) deciding on the number of rules; and 3) getting an initial estimate of parameters of the fuzzy systems. We justify that one should start with separate clustering of X (input) and Y (output). We propose a scheme to establish correspondence between the clusters obtained in X and Y. The correspondence dictates whether further splitting/merging of clusters is needed or not. If X and Y do not exhibit strong cluster substructures, then again clustering of X* (input data augmented by the output data) exploiting the results of separate clustering of X and Y, and of the correspondence scheme is recommended. We justify that usual cluster validity indices are not suitable for finding the number of rules, and the proposed scheme does not use any cluster validity index. Three methods are suggested to get the initial estimate of membership functions (MFs). The proposed scheme is used to identify the rule base needed to realize a self-tuning fuzzy PI-type controller and its performance is found to be quite satisfactory.     

A new kernel-based fuzzy clustering approach: support vector clustering with cell growing

In this paper, the support vector clustering is extended to an adaptive cell growing model which maps data points to a high dimensional feature space through a desired kernel function. This generalized model is called multiple spheres support vector clustering, which essentially identifies dense regions in the original space by finding their corresponding spheres with minimal radius in the feature space. A multisphere clustering algorithm based on adaptive cluster cell growing method is developed, whereby it is possible to obtain the grade of memberships, as well as cluster prototypes in partition. The effectiveness of the proposed algorithm is demonstrated for the problem of arbitrary cluster shapes and for prototype identification in an actual application to a handwritten digit data set.     

A heuristic error-feedback learning algorithm for fuzzy modeling

Describes a type of fuzzy system with interpolating capability to extract MISO fuzzy rules from input-output sample data through learning. The proposed model inherits many merits from Sugeno-type models and their variations. A heuristic error-feedback learning algorithm associated with the model is suggested. Based on which, the estimator is shown to have a self-adjusting step when approaching a minimum     

MOSFET mismatch modeling: a new approach

Digital and analog ICs generally rely on the concept of matched behavior between identically designed devices. Time-independent variations between identically designed transistors, called mismatch, affect the performance of most analog and even digital MOS circuits. This article focuses on the analysis of mismatch in MOS transistors resulting from random fluctuations of the dopant concentration, first studied by Keyes. Today, we recognize these fluctuations as the main cause of mismatch in bulk CMOS transistors.