Fuzzy Logic - Home - Springer978-3-322-88955...Fuzzy Logic Implementation and Applications Edited by M J Patyra University of Minnesota, USA OM Mlynek Swiss Federal Institute of Lausanne

Fuzzy Logic

Fuzzy Logic Implementation and Applications

Edited by

M J Patyra University of Minnesota, USA

OM Mlynek Swiss Federal Institute of Lausanne Switzerland

~W1LEYmTEUBNER A Partnership between John Wiley & Sons and B. G. Teubner Publishers

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Die Deutsche Bibliotheck - CIP-Einheitsaufnahme Fuzzy logic: implementation and applications 1 ed. by M. J. Patyra : D. M. Mlynek. - Stuttgart; Leipzig; Teubner; Chichester; New York; Brisbane; Toronto; Singapore: Wiley, 1996

ISBN-13: 978-3-322-88957-7 e-ISBN-13: 978-3-322-88955-3

DOl: 10.1007/978-3-322-88955-3

NE: Patyra, Marek J. (Hrsg.)

WG:37 2790

DBN 94.719152.6 nh V: Teubner

Library of Congress Cataloging in Publication Data

96.03.26

Fuzzy logic: implementation and applications 1 edited by M. J. Patyra, D. M. Mlynek.

p. cm. Includes bibliographical references and index. ISBN 0 471 95059 9 1. Automatic control. 2. Fuzzy logic. I. Patyra, M. J. (Marek 1.)

U. Mlynek, D. M. TJ213.F881996 629.8- dc20

British Library Cataloguing in Publication Data

95-45241 CIP

A catalogue record for this book is available from the British Library

Typeset in I 0/12pt Times by Thomson Press (India) Ltd, New Ddhi

This book is printed on acid-free paper responsibly manufactured from sustainable forestation for which at least two trees are planted' for each one used for paper production.

Contents

Editor's Preface

List of Contributors

Acknowledgments

THEORY 1 Fuzzy Sets in Approximate Reasoning: a Personal View

1.1 Introduction 1.2 Graduality- and Similarity-based Approximate Reasoning

1.2.1 Comparison of Fuzzy Relations, Extension Principle and Similarity 1.2.2 Interpolative Reasoning 1.2.3 Qualitative Reasoning

1.3 Uncertainty Management 1.3.1 Background 1.3.2 Uncertain Fuzzy Rules 1.3.3 Approximate Reasoning with Fuzzy Rules 1.3.4 Possibilistic Logic 1.3.5 Default Reasoning 1.3.6 Abductive Reasoning

1.4 Concluding Remarks References

FUZZY LOGIC CONTROL 2 Fuzzy Logic Control: a Systematic Design and Performance

Assessment Methodology 2.1 Introduction 2.2 The Phase Portrait Assignment Algorithm

2.2.1 Fuzzy Logic control 2.2.2 The Automatic Rule-Generation Method

2.3 Performance Assessment 2.3.1 Stability Analysis 2.3.2 Robustness Analysis

2.4 Application Examples 2.4.1 The Engine Model 2.4.2 The Fuzzy Controller 2.4.3 Simulation Results

xi

xvii

xix

1

3 3 4 4 6 9

11 12 15 18 21 24 26 32 32

37

39 39 41 41 42 49 50 51 53 53 55 59

vi CONTENTS

2.5 Stability and Robustness Results 2.6 Conclusions Acknowledgment References

3 On the Compatibility of Fuzzy Control and Conventional Control

59 61 61 62

Techniques 63 3.1 Introduction 63 3.2 Sliding Mode Fuzzy Control 65

3.2.1 The Principle of Sliding Mode Control 65 3.2.2 The Similarity Between SMC and FC 67 3.2.3 The Sliding Mode FC (SMFC) as a State-dependent Filter 68 3.2.4 Normalization and Denormalization 69 3.2.5 FC with Boundary Layer 70 3.2.6 FC of Higher Order 71 3.2.7 Numerical Example 73

3.3 Scaling of Fuzzy Controllers Using the Cross-correlation 78 3.3.1 Input-Output Correlation for an FC 81 3.3.2 Application to a Redundant Manipulator Arm 87

3.4 Fuzzy inputs 90 3.4.1 Some Useful Operations on Fuzzy Sets 91 3.4.2 The sgn-function 97 3.4.3 Sliding Mode Control and Related Control Strategies 99 3.4.4 Simulation Results 107

References 113

4 On the Crisp-type Fuzzy Controller: Behaviour Analysis and Improvement 117 4.1 Introduction 117 4.2 The Crisp-Type Fuzzy Logic Controller 118 4.3 The Dynamic Analysis of the Crisp-Type Fuzzy Controller 119 4.4 The Static Analysis of the Crisp-Type Fuzzy Control System 127 4.5 An Improvement: Pid-Type Fuzzy Controller Structure 130 4.6 Further Improvement: The Parameter Adaptive Fuzzy Controller 134 4;7 Conclusions 137 References 138

FUZZY LOGIC HARDWARE IMPLEMENTATIONS

5 Design Considerations of Digital Fuzzy Logic Controllers 5.1 Introduction 5.2 Digital-based Fuzzy Logic Hardware

5.2.1 Digital Fuzzification 5.2.2 Digital Fuzzy Inferencing 5.2.3 Digital Defuzzification

5.3 Fuzzy Logic Based Controllers 5.3.1 Digital FLC Characteristics 5.3.2 Single-Input Single-Output Fuzzy Logic Controllers 5.3.3 Double-Input Single-Output Fuzzy Logic Controller 5.3.4 Multiple-Input Single-Output Fuzzy Logic Controller 5.3.5 Multiple-Input Multiple-Output Fuzzy Logic Controller

141

143 143 144 144 146 149 151 151 153 155 157 159

CONTENTS vii

5.4 Hardware Implementation: Comparative Study 163 5.4.1 Hardware Mapping of FLC Models 164 5.4.2 Hardware Implementation Issues 171 5.4.3 Summary 172

5.5 Final Remarks 172 References 173

6 Parallel Algorithm for Fuzzy Logic Controller 177 6.1 Introduction 177 6.2 Mathematical Models for Fuzzy Model Building and Inference Computations 177

6.2.1 Single-Input Single-Output System 177 6.2.2 Multiple-Input Single-Output System 179 6.2.3 Multiple-Input Multiple-Output System 180

6.3 Parallel Algorithm 181 6.4 Conceptual Hardware Implementation 187

6.4.1 SISO System 187 6.4.2 Hardware Architectures for MISO and MIMO Systems 190 6.4.3 Fuzzy Controller Hardware Accelerator 191

6.5 Performance Characteristics 192 6.5.1 Maximum Sustainable Processing Rate 6.5.2 Improvements

6.6 Conclusions References

192 193 194 194

7 Fuzzy Flip-flop 197 7.1 Introduction 197 7.2 Outline of Binary Flip-flop and Fundamental Fuzzy Operations 198

7.2.1 A Binary Logic J-K Flip-flop 198 7.2.2 Definition of Fuzzy Negation, t-norm and s-norm 199

7.3 Definition of Fuzzy Flip-flop 201 7.4 Fuzzy Flip-flop using Complementation, Min and Max Operations 203 7.5 Fuzzy Flip-flop using Complementation, Algebraic Product and Algebraic Sum 207 7.6 Fundamentals of Implementation of the Min Max Fuzzy Flip-flop 207 7.7 Discrete and Voltage Mode Min Max Fuzzy Flip-flop Circuits 210 7.8 Fundamentals of Implementation of the Algebraic Fuzzy Flip-flop 217 7.9 Discrete and Voltage Mode Algebraic Fuzzy Flip-flop Circuits 219 7.10 Comparison of the Performance of Min Max Type Versus Algebraic

Type Fuzzy Flip-flop circuit 221 7.11 Fuzzy register circuit 222 7.12 VLSI design of the Fuzzy Register Circuit 224

7.12.1 VLSI Design ofthe Min Max Type Fuzzy Flip-flop Circuit 224 7.12.2 VLSI Design of the Fuzzy Register 230

7.13 Conclusion 235 References

8 Design Automation of Fuzzy Logic Circuits 8.1 Introduction 8.2 Basic Fuzzy Operators

8.2.1 Terminology and Resolution Principle 8.2.2 Fuzzy Inclusion as the Natural Extension of Boolean Inclusion 8.2.3 Symbolic Implementation of Fuzzy Operators

235

237 237 238 238 239 242

viii CONTENTS

8.3 CMOS Implementation 243 8.3.1 CMOS Implementation of Fuzzy Operators 243 8.3.2 Current Mirror-based Approach 244 8.3.3 Case Study: Implementation of the Min Unit 247

8.4 Fuzzy Development System 247 8.4.1 Basic Framework of the Fuzzy Logic Development Environment 248 8.4.2 Graphical Simulation Interface 249 8.4.3 Design Automation System 250 8.4.4 Netlist 252 8.4.5 Placement 256 8.4.6 Route 256 8.4.7 Superphenix 256

8.5 CMOS Fuzzy Logic-based Controller 259 8.6 Conclusion 260

8.6.1 Features of the VLSI technique taken for the Integration of Fuzzy Circuits 260 8.6.2 Improvement of the Structure of the Fuzzy Logic Development

Environment 261 Acknowledgments 262 References 262

HYBRID SYSTEMS AND APPLICATIONS 265

9 Neuro-fuzzy Systems: Hybrid Configurations 9.1 Preliminaries 9.2 Main Classes of Fuzzy Systems 9.3 Fuzzy Systems

9.3.1 Linguistic Systems and Fuzzy Systems 9.3.2 Fuzzy Systems and Memory Processes 9.3.3 Classic Neurons 9.3.4 Linear Combiners as Neurons 9.3.5 Elementary Recurrent Systems

9.4 Fuzzy Neurons 9.4.1 Elementary Fuzzy Neurons 9.4.2 Neurons with Fuzzy Weights 9.4.3 Inclusion of Fuzzy Weights into the Conventional Neuron Model

9.5 Neural Networks 9.6 Discrete Systems and Generalizations to Neuro-fuzzy Systems 9.7 Invariant Neuro-fuzzy Systems

9.7.1 Main Configurations 9.7.2 Series Neuro-fuzzy Systems and their Interpretation

9.8 Several Recurrent Neuro-fuzzy System Configurations 9.8.1 Elementary Loops: Models of Memory Effects (Output Memory) 9.8.2 Implementation of Complex Equations and Connections with

Chaos in Classic Systems 9.9 Final Remarks References

10 A Fuzzy Logic Approach to Handwriting Recognition 10.1 Introduction 10.2 Human reading 10.3 Handwriting Recognition: Current Approaches 10.4 A Fuzzy Processor for Handwriting Recognition

10.4.1 Data Extraction and Preprocessing

267 267 269 270 270 271 272 274 275 276 276 277 277 283 285 287 287 290 292 292

294 296 296

299 299 300 302 304 304

CONTENTS ix

10.4.2 The Feature Measures 305 10.4.3 The Fuzzy Recognition Process 307

10.5 Training 308 10.5.1 Fuzziness and Statistics 308

10.6 Rulebase quality 309 10.6.1 Discriminability 309 10.6.2 Usefulness of Measures and Rulebase Reduction 310 10.6.3 Completeness 310 10.6.4 Overall Quality and Self-tuning 312

10.7 Results 312 10.8 Conclusions 313 Acknowledgments 313 References 313

Index 315

Editor's Preface

This edited volume contains ten papers on the subject of fuzzy technology. Fuzzy technology emerged as a combination of fuzzy sets theory, fuzzy logic and fuzzy-based reasoning. As a technology it gained a very practical meaning through thousands of applications in different theoretical as well as practical disciplines, covering mathematics, physics, chemistry, biology, life science, social science, economy, computer science, and (foremost) electrical, electronic, mechanical, nuclear, chemical, textile, aeronautic, ocean, and many other engineering disciplines.

The goal of this book is to create an interest in fuzzy technology among researchers, engineers, professionals and students involved in the research and development in the broad area of artificial intelligence.

This book is also intended to bring the reader up-to-date in the area of implementations and applications of fuzzy technology, as well as to generate and stimulate new research ideas in this area. It may inspire and motivate the researcher in new directions, as well as creating a force for new efforts to make a fuzzy technology commonly known and used in science and engineering.

This volume appears at a time of unprecedented research interest in the field of fuzzy technology. I intentionally wrote research due to the events that have occurred during the last couple of years. To be more specific, I should describe this interest geographically. Without any doubts, it means industrial and scientific interest in Asia and Europe, but it is still 'only' a scientific interest in America. This paradox has been discussed on many occasions and is a subject of unofficial talks at almost all conferences covering fuzzy sets and fuzzy logic topics. According to industrial sources, the US market for fuzzy logic­based products 'isn't there yet'. A similar source admitted that most of the developments for fuzzy logic are going on in Asia (Japan) and Europe (Germany), mainly because 'US companies only look at the short term return', whereas Japanese and Europeans 'tend to look farther down the road'. One positive aspect of this situation is that the top management in US companies recognize tremendous opportunities for fuzzy technology, and it predicts an 'enormous market in the US within five years'. The home and popular electronic goods will mostly contribute to the success to come. On the other hand, in the area of research fuzzy technology has gained great attention due to its ability to cope with many ill-defined and/or artificial intelligence problems. Fuzzy technology has been recognized as one of the tools of so-called 'soft computing'. Neural network methods and genetic algorithms are among other tools that help in efficient problem-solving. Theory, application and implementation of fuzzy control is an arena where fuzzy technology has been most successful. This phenomenon also motivated the creation of this volume.

xii EDITOR'S PREFACE

Henceforth we expect that this volume will be of great benefit to researchers, scientists and professionals developing fuzzy logic applications and working on the enhancements ofthe theory; within the five years it may still be a source of information and inspiration to managers and engineers helping them define features for their new products.

Many authors from around the world contributed to this volume. They are currently doing research, development and implementation at the cutting edge of fuzzy technology. All the authors deserve special recognition for making this volume possible and for providing such high-quality contributions.

The material is organized in four thematic sections. The first is an introduction to the theory of fuzzy sets; the second is devoted to fuzzy logic control; the third section covers unique examples of fuzzy logic implementation; finally, the fourth presents examples of neuro-fuzzy hybrid systems and their applications.

The introductory section contains the paper by top world experts in the theory of fuzzy sets and approximate reasoning, Didier Dubois and Henri Prade from Universite Paul Sabatier, Toulouse, France. Their contribution, entitled Fuzzy Sets in Approximate Reasoning: a Personal View, is absolutely unique because it presents an extraordinarily peron sal view inside the applications of fuzzy sets in approximate reasoning.

Due to their inherent abilities, fuzzy sets are capable of modelling uncertain situations and can be instrumental in the formalization of interpolative reasoning. There are at least two major advantages that can immediately be indicated in such an approach. First, similarity-based reasoning can benefit from fuzzy sets, since similarity is usually a matter of degree. Second, fuzzy sets can represent incomplete information; hence, they can be viewed as possibility distributions and can be used to generate possibility and necessity measures to assess the degree of possibility in various statements. This paper provides a personal overview throughout the last decade resulting from the research performed jointly by both authors. In this research they have explored two interpretations of fuzziness as either the description of a gradual property or as a model of incomplete state of information. The paper is an excellent introduction and a thorough guide to possibility theory serving as a convenient framework for modelling uncertainty in a qualitative way. It provides an overview through the methods where fuzzy sets serve reasoning purposes as well as the background necessary to understand basic methodological issues.

The second section of this volume is devoted to various aspects of fuzzy logic control. The first paper in this section, Fuzzy Logic Control: a Systematic Design and Per­

formance Assessment Methodology, is written by a noble scientist and researcher G. Vachtsevanos, from Georgia Institute of Technology, Atlanta, Georgia, and is co­authored by S. Farinvata, from Ford Electronics Division, Melvindale, MI. This paper sets a milestone in the systematic analysis and design approach to fuzzy dynamic systems. The lack of mathematical rigour in the analysil> and design of fuzzy logic controllers motivated the presented research. As a result, an analytical background is laid out to avoid intuitive and ad hoc implementations offuzzy logic in control. In the design area, the proposed approach combines the approximate system modelling and heuristic approach to develop a fuzzy logic controller that is complete and robust. Three measures of performance assessment are proposed: fuzzy stability, robustness, and optimality. Fur­thermore, the main objective in these areas is to formalize the analysis and design tools and to demonstrate their effectiveness in dealing with real-world applications. Usually, when the plant dynamics are ill-defined, such a system is subject to large disturbances. The proposed methodology provides an alternative solution to the available ones.

EDITOR'S PREFACE xiii

Examples from the automotive industry (e.g. car engine model) are widely used to illustrate the analysis and design tools. For the system in hand, the fuzzy rule base was developed. This rule base accommodates the approximate state space representation of the nonlinear dynamic system. The simulation results indicate the effectiveness of the fuzzy logic control tools in terms of stability and robustness to external disturbances. This approach is, however, not free of some drawbacks: the complexity increases with the increase of the number of inputs. Also, the search through the data base becomes time-consuming for a large number of categories. The developed system can easily be integrated into existing expert systems to provide an efficient way to control fuzzy dynamic systems.

An industrial approach to solving fuzzy logic based control issues is delineated in the next paper, On the Compatibility of Fuzzy Control and Conventional Control Tech­niques. This paper was written by the experienced researcher and developer R. Palm from Siemens, Munich, Germany. This paper continues the discussion on the compatibility of the crisp and fuzzy control systems. With crisp-type fuzzy systems the main question is again related to the determination of the stability, performance and robustness of such mixed systems. As proven, the conventional linear and nonlinear control theory can contribute a great deal to the strategy defining the mixed systems. To address problems of stability, robustness and performance, the necessary translation from the 'fuzzy' world into a 'crisp' world is required. That can be used as a common basis to make a fair comparison. This paper addresses three main issues: the similarities between fuzzy control and variable structure systems with sliding modes; the representation of the fuzzy controller as a nonlinear control element and its interpretation as an equivalent gain; and noisy signals in the control loop and their interpretations as fuzzy signals. These problems are thoroughly discussed and illustrated with many simulated examples. Also it is proved that there is a substantial similarity between fuzzy and conventional nonlinear control.

In the paper entitled On the Crisp-type Fuzzy Controller: Behaviour Analysis and Improvement, written by W. Z. Qiao and co-authored by one of the Japanese pioneer in fuzzy logic research and application, M. Mizumoto from Osaka Electro- Communication University, Nayagawa, Osaka, Japan, one specific type offuzzy logic controller, the crisp fuzzy controller, is analyzed. Due to its simplicity, the crisp fuzzy controller has been widely used in a variety of industrial applications. In this type of controller the antecedent part offuzzy control rules is standard (i.e. defined by a fuzzy set) but the consequent parts of these rules are crisp numbers as opposed to the classic fuzzy controller. The authors focus on the dynamic behaviour of such controllers. They studied the input-output characteristics of crisp-type fuzzy controllers with min-max and product-sum inference methods used. As discovered, both kinds of crisp fuzzy controllers have very similar input-output characteristics and the differences between them are minor. Also, the crisp-type fuzzy controller can be regarded as a parameter time varying PD controller. As a result, the analysis and design of fuzzy control systems can be performed with con­ventional PID control methodology. As shown previously the PD type fuzzy controller yields a steady-state error for the 'zero' system. This error can be eliminated with PI type fuzzy controller. The authors propose a structure that combines features of both PD type and PI type fuzzy controllers. Such a PID type fuzzy controller allows the control system to have a fast rise time and a small overshoot, as well as a shorter settling time than the PD or PI controllers. To further improve the performance of the proposed PID controller, the authors designed a parameter adaptive fuzzy controller. This controller decreases the

xiv EDITOR'S PEFACE

equivalent integral control component of the fuzzy controller gradually with the system response process time. This is to increase the dumping of the system when the system is about to settle down, while keeping the proportional control component unchanged to guarantee the fast reaction against the system's error. For the parameter adaptive fuzzy controller, the oscillations of the system are strongly rejected and the settling time is substantially reduced. The presented results of the analysis and simulation of parameter adaptive fuzzy controller can be used to guide the design of more sophisticated fuzzy logic-based control systems.

The third section of this volume, Fuzzy Logic Hardware Implementations, provides an overview of state-of-the-art techniques that are used for the hardware implementations of fuzzy logic-based circuits and systems.

The paper written by M. Patyra from the University of Minnesota, Duluth, MN, is entitled Design Considerations of Digital Fuzzy Logic Controllers, and presents an overview of the design issues related to the digital implementations of fuzzy logic-based controllers. Fuzzy logic controllers are chosen for their unquestionable success in the area of applications and implementations offuzzy technology. Since 1985 when the first digital implementation of a fuzzy logic controller emerged, there have been many successful implementations reported in the technical literature. Although common by means of used digital techniques, many of these implementations are hard to compare in terms of characteristic features.

The purpose of this paper is twofold. First, this paper provides a unified framework for the comparison of digital fuzzy logic controllers. Second, it presents an analytical formulation of hardware cost and performance of various configurations used to imple­ment these controllers. This paper also looks into the most commonly used controller configurations and shows the fuzzy algorithms mapping into hardware. As recent developments show, digital fuzzy logic controllers could become inherent parts oflarger­hierarchical control systems incorporating various technologies including classic control, neural networks and genetic algorithms.

The next paper in this section, entitled Parallel Algorithm for Fuzzy Logic Controller, is written by J. L. Grantner from Western Michigan University, Kalamazoo, MI. It discusses in great detail some of the issues mentioned in the previous paper. In this paper a parallel algorithm to build a fuzzy model and execute the fuzzy inference is proposed. Based on this algorithm, the inference engine and a conceptual hardware implemen­tations for a high-speed fuzzy logic controller are discussed. The characteristic features of the algorithm include a high degree of parallelism in performing fuzzy operations, constant low memory requirement to store the complete knowledge base (independent of the number of rules), error detection in case the linguistic model fails, flexibility in supporting SISO, MISO and MIMO systems, and a convenient natural way of map­ping the algorithm into the hardware structure. The presented approach allows the creation and a storage of the compact rule base. By analyzing the mathematical models for SISO, MISO and MIMO systems it shows that a single algorithm can be developed to parametrize the inputs and outputs to the controller, according to the operation to be executed (model building or fuzzy inference). As a result, the parallel architecture is proposed for the controller hardware accelerator which features a maximum sustainable performance. This architecture is implemented with the pipeline technique to ensure a high degree of hardware usability and boost perfor­mance.

EDITOR'S PREFACE xv

The next paper, entitled Fuzzy Flip-flop, is written by world class experts who have been in the field of fuzzy technology since its very beginning: K. Ozawa and K. Hirota (Hosei University, Tokyo, Japan) and L. T. Koczy (Technical University of Budapest, Hungary). This paper is dedicated to a special class of digital fuzzy logic circuits, fuzzy flip-flops. As pointed out by the authors, a great deal of research has been devoted to the realization of the idea of a fuzzy computer. However, a few types of fuzzy inference engines (which are also called fuzzy processors) were prepared and implemented by Yamakawa, Tigai and Watanabe. Although these fuzzy inference devices opened a new realm of opportunity for fuzzy logic, especially in control applications, they performed basically a single step inference. In order to realize multistep inference, fuzzy memory modules are required. This motivated the research of which the results are described in this paper. The authors propose and define a fuzzy flip-flop which is an extension of the classic binary flip-flop, specifically a J-K flip flop. They formulate a truth table for the fuzzy J-K flip flop where binary negation, union, and intersection operations are extended by means offuzzy negation, t-norm, and s-norm, respectively. Reset type and set type of equations for fuzzy J-K flip flop are formulated, and the results are graphically illustrated with respect to different t-norm and s-norm representations. These representations include fuzzy comple­ment, minimum, maximum, algebraic product, and algebraic sum operations. The hardware implementation of a fuzzy J-K flip-flop with standard logic devices is also presented. These circuits are functionally tested and the results are illustrated. The results from the circuit testing also suggest a possible and efficient VLSI implementation for the fuzzy J-K flip-flops, as well as for more sophisticated circuits built from them, such as fuzzy registers and fuzzy memories.

The paper entitled Design of Fuzzy Logic Circuits, by L. Lemaitre from the Swiss Federal Institute of Technology, Lausanne, describes the methodology of generating structures for complex fuzzy logic circuits based on specified fuzzy functions. The methodology is based on the introduction of basic fuzzy operators. These operators have their immediate and simple representation in hardware, namely CMOS circuit represen­tations. With such a background built up the design automation system takes the description of the fuzzy function and converts it into the form represented by basic operators. Such a form is ready to be used to generate a CMOS layout for the circuit performing the operations defined by a function in hand. The design automation system places the layout elements and solves the routing problems associated with the layout optimization. The optimization is performed on two levels, local and global. With such powerful tools in hand the current-mode analogue fuzzy logic controller was synthesized, developed and manufactured. The final chip reached a performance of lOMFLIPS while occupying only OAmm2 of silicon area.

In the fourth section Hybrid Systems and Applications the first paper, entitled. Neuro-fuzzy Systems: Hybrid Configurations, gives a thorough overview of neuro-fuzzy systems. Written by two experts currently specializing in neuro-fuzzy systems, H.-N. L. Teodorescu from the Technical University ofIasi, Romania, and T. Yamakawa from the Kyushu Institute of Technology, Iizuka, Fukuoka, Japan, this paper provides a systematic discussion of hybrid configurations of neuro-fuzzy systems. The merging of these two types of systems is possible due to the functional similarities that these systems feature. Five classes of neuro-fuzzy systems are selected based on their structure. The structure of neuro-fuzzy systems can be put into the following categories: neural network structure with fuzzy logic neurons, adaptive fuzzy systems that can be modified by the neural

xvi EDITOR'S PREFACE

network during the learning process, classic neural network with the learning process determined by a fuzzy system, systems that are composed of independent neural networks and fuzzy systems, systems with neural network configurations that use fuzzy systems as neurons, and finally systems that are created by a mixture of two or more of the above systems. This paper discusses in detail three classes of systems; namely, neural network structures with fuzy logic neurons, systems that are composed of independent neural networks and fuzzy systems, and systems with neural network configurations that uses fuzzy systems as neurons. Such systems can be useful in various applications including the modelling of complex, empirical-driven processes, control of complex systems, pattern recognition and chaotic systems. Several examples of applications of such systems based upon the authors research results are provided.

A very interesting example of the direct application of fuzzy system is presented in the paper A Fuzzy Logic Approach to Handwriting Recognition. Written by D. J. Ostrowski and P. Y. K. Cheung from Imperial College, University of London, UK, this paper provides in-depth experience with fuzzy logic applied to the handwriting recognition problem. This paper describes the application offuzzy logic to cursive script recognition. Handwriting recognition is crucial for many automated task problems. The fundamental problem of cursive script is segregation because the nature of cursive script makes reliable recognition of individual letters extremely difficult. Therefore, the use of prototypical models is not satisfactory. On the other hand, the cursive script recognition is a sophisti­cated process complexed by a variability ofthe handwriting of a particular individual. The approach described in this paper consists of recognizing letters in terms of the features of the individual letter and accepting that the feature separation is unreliable. The proposed solution to this issue uses the fuzzy rule-based approach. Such a rule base is capable of accepting the variability of data and its unreliable extraction from the original images. Moreover, it derives the characters features and ability to differentiate letters from training. This paper provides a brief description of current methods of machine recogni­tion and fuzzy logic approach to such problems as w'ell;.The training of the rule base is discussed in detail. Finally, the examples are shown along with the statistical results obtained from the benchmark data set provided by the UNIPEN project.

Finally, the Editors wish the reader many educational, professional and fruitful experiences while studying this volume.

Marek J. Patyra Duluth, Minnesota

1995

List of Contributors

Dominic Ostrowski and Peter Cheung Department of Electrical and Electronic Engineering Imperial College Exhibition Road London SW7 2BT, UK

Didier Dubois and Henri Prade IRIT Universite Paul Sabatier 118 Rue de Narbonne 31062 Toulouse Cedex France

Shehu Farinwata Ford Research Laboratory Dearborn, MI48121-2053 USA

Kaoru Hirota Department of Systems Science Tokyo Institute of Technology Tokyo Japan

Kazuhiro Ozawa Department of Instrument and Control Engineering Hosei University 3-7-2 Kajino-cho Koganei-city, Tokyo 184, Japan

Laszlo Koczy Department of Telecommunications and Telematics Technical University of Budapest, Stoczek u.2 H-llll Budapest Hungary

Rainer Palm Corporate Research and Development Siemens AG Otto-Hahn-Ring 6 8000 Munich 83 Germany

Marek Patyra Department of Electrical and

Computer Engineering University of Minnesota Duluth, MN 55812-2496 USA

George Vachtsevanos School of Electrical Engineering Georgia Institute of Technology Atlanta, GA 30332-0250 USA

Wu Zhi Quiao and Masaharu Mizumoto Department of Management Engineering Osaka Electro-Communication University Neyagawa, Osaka 572 Japan

xviii L 1ST OF CONTRIBUTORS

Laurent Lemaitre Department of Computer Science University of California Berkeley, CA 94720-1776 USA

Janos Grantner Department of Electrical Engineering Western Michigan University Kalamazoo, MI 49008-5066 USA

H.-N.L. Teodorescu Technical University of 1 asi I asi, Romania

T. Yamakawa Kyushu Institute of Technology lizuka, Fukuoka Japan

Acknowledgments

We are grateful to the staff of John Wiley and Sons, Europe for their advice, dedication and commitment to this project. Their high-quality assistance has made the production of this volume smooth and undisturbed. We would like to express our appreciation especially, to Anne-Marie Halligan and Peter Mitchell. Without their professional guidance and support, publication of this volurne would have been almost impossible.