Showing papers on "Neuro-fuzzy published in 2008"

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

Abstract: This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi-Sugeno-Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.

Computational Intelligence: Methods and Techniques

Abstract: This book focuses on various techniques of computational intelligence, both single ones and those which form hybrid methods. Those techniques are today commonly applied issues of artificial intelligence, e.g. to process speech and natural language, build expert systems and robots. The first part of the book presents methods of knowledge representation using different techniques, namely the rough sets, type-1 fuzzy sets and type-2 fuzzy sets. Next various neural network architectures are presented and their learning algorithms are derived. Moreover, the family of evolutionary algorithms is discussed, in particular the classical genetic algorithm, evolutionary strategies and genetic programming, including connections between these techniques and neural networks and fuzzy systems. In the last part of the book, various methods of data partitioning and algorithms of automatic data clustering are given and new neuro-fuzzy architectures are studied and compared.

Fuzzy Wavelet Neural Networks for Identification and Control of Dynamic Plants—A Novel Structure and a Comparative Study

Abstract: One of the main problems for effective control of an uncertain system is the creation of the proper knowledge base for the control system. In this paper, the integration of fuzzy set theory and wavelet neural networks (WNNs) is proposed to alleviate the problem. The proposed fuzzy WNN is constructed on the base of a set of fuzzy rules. Each rule includes a wavelet function in the consequent part of the rule. The parameter update rules of the system are derived based on the gradient descent method. The structure is tested for the identification and the control of the dynamic plants commonly used in the literature. It is seen that the proposed structure results in a better performance despite its smaller parameter space.

Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications

Abstract: The main subject of this book is the fuzzy c-means proposed by Dunn and Bezdek and their variations including recent studies A main reason why we concentrate on fuzzy c-means is that most methodology and application studies in fuzzy clustering use fuzzy c-means, and hence fuzzy c-means should be considered to be a major technique of clustering in general, regardless whether one is interested in fuzzy methods or not Unlike most studies in fuzzy c-means, what we emphasize in this book is a family of algorithms using entropy or entropy-regularized methods which are less known, but we consider the entropy-based method to be another useful method of fuzzy c-means Throughout this book one of our intentions is to uncover theoretical and methodological differences between the Dunn and Bezdek traditional method and the entropy-based method We do note claim that the entropy-based method is better than the traditional method, but we believe that the methods of fuzzy c-means become complete by adding the entropy-based method to the method by Dunn and Bezdek, since we can observe natures of the both methods more deeply by contrasting these two

Fuzzy Interpolation and Extrapolation: A Practical Approach

Abstract: Fuzzy interpolation does not only help to reduce the complexity of fuzzy models, but also makes inference in sparse rule-based systems possible. It has been successfully applied to systems control, but limited work exists for its applications to tasks like prediction and classification. Almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation, and that such rules must flank the observation for each attribute. Also, some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes. To avoid such limitations and develop a more practical approach, this paper extends the work of Huang and Shen. The result enables both interpolation and extrapolation which involve multiple fuzzy rules, with each rule consisting of multiple antecedents. Two realistic applications, namely truck backer-upper control and computer activity prediction, are provided in this paper to demonstrate the utility of the extended approach. Experiment-based comparisons to the most commonly used Mamdani fuzzy reasoning mechanism, and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research.

Fuzzy Modeling and Fuzzy Control

Abstract: preparation of statements that are fair, clear, and helpful to courts; and responding to questions by judges and juries.” The author does a good job of meeting these goals through discussions on how to quantify DNA evidence for presentation in court or preparing legal statements. This book will be helpful to statisticians and others with technical backgrounds, who might be called on as expert witnesses in deciding what kind of information is considered a valid evidence and what should be presented. For example, in Chapter 8, the author mentions that an expert witness needs sufficient information to answer two questions for a jury: (1) How likely is the evidence if the defendant s is guilty? and (2) how likely is the evidence if s is innocent and i is the true culprit? The author discusses different ways to answer these questions. Although the writing in this book is fairly nontechnical, some mathematical theory behind the results is presented, but not for courtroom statements. It is given for forensic scientists to provide insight into the reasoning behind results. The concept of p-value is very difficult to understand for those unfamiliar with statistical terminology. The author presents this concept in plain English in very easy-to-understand language without actually mentioning the term “pvalue.” Although the concepts of hypotheses testing are used in discussions from the beginning, it is introduced formally only at the end of Chapter 8, where the standard definition of p-value also is given. Similarly, the discussions include descriptions of the concepts of conditional probabilities and two types of error rates, which also are not easy to understand for members of a jury. The errors of logic, referred to as the prosecutor’s fallacy and the defendant’s fallacy, are described using simple examples. An interesting discussion also shows how a lower level of language comprehension by jurors can lead to confusion about differences in P(A|B) and P(B|A). There is more emphasis on evaluating evidence using likelihood ratios and the Bayes theorem. In today’s world of expanding use of scientific methods to resolve conflicts by the judicial system and recent increases in use of DNA profiling as evidence, there is a need for more literature that describes these concepts in simple language. This book is a good example of how statistics can be explained in plain English to a nontechnical audience, a skill that every statistician needs to master for improved communication.

An Integrated Neural Fuzzy Approach for Fault Diagnosis of Transformers

Abstract: This paper presents a new and efficient integrated neural fuzzy approach for transformer fault diagnosis using dissolved gas analysis. The proposed approach formulates the modeling problem of higher dimensions into lower dimensions by using the input feature selection based on competitive learning and neural fuzzy model. Then, the fuzzy rule base for the identification of fault is designed by applying the subtractive clustering method which is very good at handling the noisy input data. Verification of the proposed approach has been carried out by testing on standard and practical data. In comparison to the results obtained from the existing conventional and neural fuzzy techniques, the proposed method has been shown to possess superior performance in identifying the transformer fault type.

Nonlinear network structures for feedback control

Abstract: A framework is given for controller design using Nonlinear Network Structures, which include both neural networks and fuzzy logic systems. These structures possess a universal approximation property that allows them to be used in feedback control of unknown systems without requirements for linearity in the system parameters or finding a regression matrix. Nonlinear nets can be linear or nonlinear in the tunable weight parameters. In the latter case weight tuning algorithms are not straightforward to obtain. Feedback control topologies and weight tuning algorithms are given here that guarantee closed-loop stability and bounded weights. Extensions are discussed to force control, backstepping control, and output feedback control, where dynamic nonlinear nets are required.

Fuzzy Interpolative Reasoning for Sparse Fuzzy-Rule-Based Systems Based on the Areas of Fuzzy Sets

Abstract: Fuzzy interpolative reasoning is an inference technique for dealing with the sparse rules problem in sparse fuzzy-rule-based systems. In this paper, we present a new fuzzy interpolative reasoning method for sparse fuzzy-rule-based systems based on the areas of fuzzy sets. The proposed method uses the weighted average method to infer the fuzzy interpolative reasoning results and has the following advantages: (1) it holds the normality and the convexity of the fuzzy interpolative reasoning result, (2) it can deal with fuzzy interpolative reasoning with complicated membership functions, (3) it can deal with fuzzy interpolative reasoning when the fuzzy sets of the antecedents and the consequents of the fuzzy rules have different kinds of membership functions, (4) it can handle fuzzy interpolative reasoning with multiple antecedent variables, (5) it can handle fuzzy interpolative reasoning with multiple fuzzy rules, and (6) it can handle fuzzy interpolative reasoning with logically consistent properties with respect to the ratios of fuzziness. We use some examples to compare the fuzzy interpolative reasoning results of the proposed method with those of the existing fuzzy interpolative reasoning methods. In terms of the six evaluation indices, the experimental results show that the proposed method performs more reasonably than the existing methods. The proposed method provides us a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy-rule-based systems.

Fuzzy Modeling with Spatial Information for Geographic Problems

Abstract: Reasoning About Regions, Relations, and Fields.- Fuzzy Reasoning about Geographic Regions.- Combined Extraction of Directional and Topological Relationship Information from 2D Concave Objects.- Field Based Methods for the Modeling of Fuzzy Spatial Data.- Modeling Localities with Fuzzy Sets and GIS.- Fuzzy Classification.- Mining Weather Data Using Fuzzy Cluster Analysis.- Modelling the Fuzzy Spatial Extent of Geographical Entities.- Multi-Dimensional Interpolations with Fuzzy Sets.- Talking Space - A Social & Fuzzy Logical GIS Perspective On Modelling Spatial Dynamics.- A Valuation of the Reliability of a GIS Based on the Fuzzy Logic in a Concrete Case Study.- Fuzzy Representations of Landscape Features.- Fuzziness and Ambiguity in Multi-Scale Analysis of Landscape Morphometry.- Fuzzy Representation of Special Terrain Features Using a Similarity-based Approach.- Decision Making with GIS and Fuzzy Sets.- Spatial Decision-Making Using Fuzzy Decision Tables: Theory, Application and Limitations.- Spatial Decision Making Using Fuzzy GIS.- Spatially Explicit Individual-Based Ecological Modeling with Mobile Fuzzy Agents.

Application of evolving Takagi-Sugeno fuzzy model to nonlinear system identification

Abstract: In this paper, a new encoding scheme is presented for learning the Takagi-Sugeno (T-S) fuzzy model from data by genetic algorithms (GAs). In the proposed encoding scheme, the rule structure (selection of rules and number of rules), the input structure (selection of inputs and number of inputs), and the antecedent membership function (MF) parameters of the T-S fuzzy model are all represented in one chromosome and evolved together such that the optimisation of rule structure, input structure, and MF parameters can be achieved simultaneously. The performance of the developed evolving T-S fuzzy model is first validated by studying the benchmark Box-Jenkins nonlinear system identification problem and nonlinear plant modelling problem, and comparing the obtained results with other existing results. Then, it is applied to approximate the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper of which identification problem is significantly difficult due to its inherently hysteretic and highly nonlinear dynamics. It is shown by the validation applications that the developed evolving T-S fuzzy model can identify the nonlinear system satisfactorily with acceptable number of rules and appropriate inputs.

Chaos synchronization using fuzzy logic controller

Abstract: The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master–slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing–Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.

Fuzzy risk analysis based on measures of similarity between interval-valued fuzzy numbers

Abstract: In this paper, we present a new method for handling fuzzy risk analysis problems based on measures of similarity between interval-valued fuzzy numbers. First, we propose a similarity measure to calculate the degree of similarity between interval-valued fuzzy numbers. The proposed similarity measure uses the concept of geometry to calculate the center-of-gravity (COG) points of the lower fuzzy numbers and the upper fuzzy numbers of interval-valued fuzzy numbers, respectively, to calculate the degree of similarity between interval-valued fuzzy numbers. We also prove some properties of the proposed similarity measure. Then, we use the proposed similarity measure for interval-valued fuzzy numbers for handling fuzzy risk analysis problems. The proposed method is more flexible and more intelligent than the methods presented in [S.J. Chen, S.M. Chen, Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers, IEEE Transactions on Fuzzy Systems 11 (1) (2003) 45-56; S.M. Chen, Evaluating the rate of aggregative risk in software development using fuzzy set theory, Cybernetics and Systems 30 (1) (1999) 57-75; S.M. Chen, New methods for subjective mental workload assessment and fuzzy risk analysis, Cybernetics and Systems 27 (5) (1996) 449-472; H.M. Lee, Applying fuzzy set theory to evaluate the rate of aggregative risk in software development, Fuzzy Sets and Systems 79 (3) (1996) 323-336; K.J. Schmucker, Fuzzy Sets, Natural Language Computations, and Risk Analysis, Computer Science Press, MD (1984)] due to the fact that it uses interval-valued fuzzy numbers rather than fuzzy numbers or generalized fuzzy numbers for handling fuzzy risk analysis problems. It provides us with a useful way for handling fuzzy risk analysis problems.

Augmented Stable Fuzzy Control for Flexible Robotic Arm Using LMI Approach and Neuro-Fuzzy State Space Modeling

Abstract: Designing the control strategy for a flexible robotic arm has long been considered a complex problem as it requires stabilizing the vibration simultaneously with the primary objective of position control. A stable state-feedback fuzzy controller is proposed here for such a flexible arm. The controller is designed on the basis of a neuro-fuzzy state-space model that is successfully trained using the experimental data acquired from a real robotic arm. The complex problem of solving stability conditions is taken care of by recasting them in the form of linear matrix inequalities and then solving them using a popular interior-point-based method. This asymptotically stable fuzzy controller is further augmented to provide enhanced transient performance along with maintaining the excellent steady-state performance shown by the stable control strategy. The controller hence designed has been successfully implemented for a real robotic arm to operate over a long angular range of 180 with several payload conditions and, for situations where the system is operated for a long range and with a large variation in payload conditions, it could successfully outperform the recently proposed proportional derivative and strain controller.

Fuzzy polynomial neural networks for approximation of the compressive strength of concrete

Abstract: The main purpose of this paper is to develop fuzzy polynomial neural networks (FPNN) to predict the compressive strength of concrete. Two different architectures of FPNN are addressed (Type1 and Type2) and their training methods are discussed. In this research, the proposed FPNN is a combination of fuzzy neural networks (FNNs) and polynomial neural networks (PNNs). Here, while the FNN demonstrates the premises (If-Part) of the fuzzy model, the PNN is implemented as its consequence (Then-Part). To enhance the performance of the network, back propagation (BP), and list square error (LSE) algorithms are utilized for the tuning of the system. Six different FPNN architectures are constructed, trained, and tested using the experimental data of 458 different concrete mix-designs collected from three distinct sources. The data are organized in a format of six input parameters of concrete ingredients and one output as 28-day compressive strength of the mix-design. Using root means square (RMS) and correlation factors (CFs), the models are evaluated and compared with training and testing data pairs. The results show that FPNN-Type1 has strong potential as a feasible tool for prediction of the compressive strength of concrete mix-design. However, the FPNN-Type2 is recognized as unfeasible model to this purpose.

A Type-2 Self-Organizing Neural Fuzzy System and Its FPGA Implementation

Abstract: This paper proposes a type-2 self-organizing neural fuzzy system (T2SONFS) and its hardware implementation. The antecedent parts in each T2SONFS fuzzy rule are interval type-2 fuzzy sets, and the consequent part is of Mamdani type. Using interval type-2 fuzzy sets in T2SONFS enables it to be more robust than type-1 fuzzy systems. T2SONFS learning consists of structure and parameter identification. For structure identification, an online clustering algorithm is proposed to generate rules automatically and flexibly distribute them in the input space. For parameter identification, a rule-ordered Kalman filter algorithm is proposed to tune the consequent-part parameters. The learned T2SONFS is hardware implemented, and implementation techniques are proposed to simplify the complex computation process of a type-2 fuzzy system. The T2SONFS is applied to nonlinear system identification and truck backing control problems with clean and noisy training data. Comparisons between type-1 and type-2 neural fuzzy systems verify the learning ability and robustness of the T2SONFS. The learned T2SONFS is hardware implemented in a field-programmable gate array chip to verify functionality of the designed circuits.

Fuzzy Logic and Applications

Abstract: Cluster analysis of high-dimensional data has become of special interest in recent years. The term high-dimensional data can refer to a larger number of attributes – 20 or more – as they often occur in database tables. But high-dimensional data can also mean that we have to deal with thousands of attributes as in the context of genomics or proteomics data where thousands of genes or proteins are measured and are considered in some analysis tasks as attributes. A main reason, why cluster analysis of high-dimensional data is different from clustering low-dimensional data, is the concentration of norm phenomenon, which states more or less that the relative differences between distances between randomly distributed points tend to be more and more similar in higher dimensions. On the one hand, fuzzy cluster analysis has been shown to be less sensitive to initialisation than, for instance, the classical k-means algorithm. On the other, standard fuzzy clustering is stronger affected by the concentration of norm phenomenon and tends to fail easily in high dimensions. Here we present a review of why fuzzy clustering has special problems with high-dimensional data and how this can be amended by modifying the fuzzifier concept. We also describe a recently introduced approach based on correlation and an attribute selection fuzzy clustering technique that can be applied when clusters can only be found in lower dimensions.

Fuzzy Interpolative Reasoning for Sparse Fuzzy Rule-Based Systems Based on ${\bm \alpha}$ -Cuts and Transformations Techniques

Abstract: In sparse fuzzy rule-based systems, the fuzzy rule bases are usually incomplete. In this situation, the system may not properly perform fuzzy reasoning to get reasonable consequences. In order to overcome the drawback of sparse fuzzy rule-based systems, there is an increasing demand to develop fuzzy interpolative reasoning techniques in sparse fuzzy rule-based systems. In this paper, we present a new fuzzy interpolative reasoning method via cutting and transformation techniques for sparse fuzzy rule-based systems. It can produce more reasonable results than the existing methods. The proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule-based systems.

Systematic design of a stable type-2 fuzzy logic controller

Abstract: Stability is one of the more important aspects in the traditional knowledge of automatic control. Type-2 fuzzy logic is an emerging and promising area for achieving intelligent control (in this case, fuzzy control). In this work we use the fuzzy Lyapunov synthesis as proposed by Margaliot and Langholz [M. Margaliot, G. Langholz, New Approaches to Fuzzy Modeling and Control: Design and Analysis, World Scientific, Singapore, 2000] to build a Lyapunov stable type-1 fuzzy logic control system, and then we make an extension from a type-1 to a type-2 fuzzy logic control system, ensuring the stability on the control system and proving the robustness of the corresponding fuzzy controller.

Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index

Abstract: Context adaptation (CA) based on evolutionary algorithms is certainly a promising approach to the development of fuzzy rule-based systems (FRBSs). In CA, a context-free model is instantiated to a context-adapted FRBS so as to increase accuracy. A typical requirement in CA is that the context-adapted system maintains the same interpretability as the context-free model, a challenging constraint given that accuracy and interpretability are often conflicting objectives. Furthermore, interpretability is difficult to quantify because of its very nature of being a qualitative concept. In this paper, we first introduce a novel index based on fuzzy ordering relations in order to provide a measure of interpretability. Then, we use the proposed index and the mean square error as goals of a multi-objective evolutionary algorithm aimed at generating a set of Pareto-optimum context-adapted Mamdani-type FRBSs with different trade-offs between accuracy and interpretability. CA is obtained through the use of specifically designed operators that adjust the universe of the input and output variables, and modify the core, the support and the shape of fuzzy sets characterizing the partitions of these universes. Finally, we show results obtained by using our approach on synthetic and real data sets.

Neuro-Fuzzy based Approach for Inverse Kinematics Solution of Industrial Robot Manipulators

Abstract: Obtaining the joint variables that result in a desired position of the robot end-effector called as inverse kinematics is one of the most important problems in robot kinematics and control. As the complexity of robot increases, obtaining the inverse kinematics solution requires the solution of non linear equations having transcendental functions are difficult and computationally expensive. In this paper, using the ability of ANFIS (Adaptive Neuro-Fuzzy Inference System) to learn from training data, it is possible to create ANFIS, an implementation of a representative fuzzy inference system using a BP neural network-like structure, with limited mathematical representation of the system. Computer simulations conducted on 2 DOF and 3DOF robot manipulator shows the effectiveness of the approach.