FUZZY HARDWARE - Springer

FUZZY HARDWARE

Architectures and Applications

FUZZY HARDWARE

Architectures and Applications

edited by

Abraham Kandel Department of Computer Science and Engineering

University ofSouth F/orida, Tampa &

Department ofElectrical Engineering-Systems Tel-Aviv University, Israel

and

Gideon Langholz Department of Electrical Engineering-Systems

Tel-Aviv University, Israel

~.

" Springer Science+Business Media, LLC

Library of Congress Cataloging-in-Publication Data

A C.I.P. Catalogue record for this book is available from. the Library of Congress.

ISBN 978-1-4613-6831-1 ISBN 978-1-4615-4090-8 (eBook) DOI 10.1007/978-1-4615-4090-8

Copyright © 1998 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers, New York in 1998 Softcover reprint of the hardcover Ist edition 1998 AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or othetwise, without the prior written permis sion ofthe publisher, Springer Science+Business Media, LLC

Printed on acid-free paper.

CONTENTS

PREFACE xv

Chapter 1 Fuzzy Hardware Research From Historical Point of View Marco Russo 1

1. Introduction 2 2. Fuzzy Processors and Fuzzy Controllers 4

2.1 Implementation choices offuzzy systems 4 2.2 Dedicated fuzzy machines 5 2.3 Other kinds of work 10 2.4 Current and future trends in fuzzy processor design 10

3. Dedicated Analog and Hybrid Circuits 11 3.1 Minimum and maximum circuits 11 3.2 Possible implementation of an analog-discrete min and

max circuit 15 3.3 Membership function circuits 15 3.4 Defuzzifiers 16 3.5 More advanced research results 18 3.6 Other kinds of work 18

4. Conclusions 19 References 20

Chapter 2 Three Generations of Fuzzy Hardware Liliane Peters and Shuwei Gou

1. Fuzzy Theory and Fuzzy Logic Control 28 2. Fuzzy Hardware - A Brief Overview 30 3. Some General Implementation Aspects 31

27

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4. The GMD Fuzzy Controllers 32 4.1 Fuzzy membership function 33 4.2 Fuzzy inference engine 35 4.3 Defuzzification 37 4.4 Knowledge base 38 4.5 Test results 38

5. Intelligent System Design 39 6. Conclusion 40 References 41

Chapter 3 Hardware Realization of Fuzzy Neural Networks C. Hart Poskar, Peter J. Czezowski, and Witold Pedrycz 43

1. Introductory Remarks 44 2. Background for Fuzzy Neural Networks 44

2.1 Fuzzy computation with logic neurons 45 2.2 Excitatory vs. Inhibitory Characteristics 48 2.3 Realization of Fuzzy Neurons 48

3. Fuzzy Neural Learning 50 3.1 Learning with referential neurons 51

4. RFN - General Design 57 4.1 The reconfigurable fuzzy processor 57 4.2 The learning unit 62 4.3 The memory unit 63

5. The Network Design 64 5.1 The logic unit 64 5.2 The interconnection network 65 5.3 The interface 67

6. Hardware Implementation 68 6.1 Referential computation unit 68 6.2 Aggregative neuron design 70 6.3 Implementing the learning unit 71

7. Concluding Remarks 74 References 75

Chapter 4 AFAN - A Tool for the Automatic Design of Digital and Analog Neuro-Fuzzy Controllers Ramon Gonzalez Carvajal, Miguel A. Aguirre Echanova, Antonio J. Torralba Silgado, and Leopoldo Garcia Franquelo 77

1. Introduction 78 2. AF AN Design Flow 78

3. Architectural Issues 80 4. Some Examples 81 5. The Analog Approach 86 6. Conclusions and Future Research 87 References 87

Chapter 5 Silicon Compilation of Fuzzy Hardware Systems Based on Generic LR Fuzzy Cells

vii

Yau-Hwang Kuo and Chao-Lieh Chen 91

1. Introduction 92 2. Generic LR Fuzzy Cells 93 3. Synthesis of Various Fuzzy Systems 95

3.1 Design of LR fuzzy cell library 96 3.2 Inference methods 97 3.3 Inference chains 103 3.4 Fuzzy neuron 105

4. The LR Fuzzy Cell-Based Silicon Compiler 107 5. Simulations and Evaluations 111 6. Conclusions 115 References 115

Chapter 6 Serial Architectures for Efficient Digital Fuzzy Hardware Processing Luis de Salvador Carrasco and Julio Gutierrez-Rios 117

1. Introduction 118 1.1 The processing of fuzzy rule-based systems 118 1.2 Universality of the fuzzy processor 118 1.3 Fuzzy processing common solutions 119

2. Brief Analysis of the Fuzzy Processing Problem 120 2.1 Data volume analysis 120 2.2 Synthesis methodologies 120 2.3 Modularity in the fuzzy processor 121 2.4 Upgrading the functionality of the fuzzy processor 122 2.5 Modifiers 122

3. Strategies to Avoid the Fuzzy Processing Problem 126 4. Architecture of an Inference Unit 126

4.1 The max-min process 127 4.2 Lukasiewicz implementation 132 4.3 Other operators 137 4.4 Systolic implementations 138

5. Modifier Architectures 138

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5.1 Modifiers of comparison in hardware 139 5.2 Modifier of translation in hardware 141 5.3 Modifiers of transformation in hardware 143

6. Defuzzification Serial Architecture 146 6.1 Singleton algorithm 147 6.2 Denominator inversion 148


Chapter 7 Automatic Implementation'bfPiecewise-Linear Fuzzy Systems Addressing Memory-Performance Trade-Off Riccardo Rovatti, Alberto Ferrari, and Michele Borgatti 159

1. Introduction 160 2. Piecewise-Linear Fuzzy Systems 161 3. An O(nlogn) Inference Procedure 162 4. An Intelligent Memory Management Unit 164 5. The Overall Architecture 169 6. Performance Optimization and Comparison 173 7. Conclusion 177 References 178 Appendix 179

Chapter 8 A Parallel Processor Architecture for Real-Time Fuzzy Applications

Giuseppe Ascia and Vincenzo Catania 181

1. Introduction 182 2. Considerations on Fuzzy Inference 183

2.1 Parallelism 183 2.2 Antecedent repetition 183 2.3 Active rules 184

3. Representation of a Fuzzy Set 184 4. Computation of the Degree of Truth of an Antecedent 185 5. Processing Fuzzy Rules 186 6. Hardware Architecture of the Processor 188

6.1 Detection unit 189 6.2 ANT-unit 189 6.3 Rule unit 191

7. Cost and Performances 193 8. Conclusions 194 References 194

Chapter 9 Short Time Decision VLSI Fuzzy Processor Alessandro Gabrielli, Enzo Gandolfi, and Massimo Masetti

1. Introduction 198 2. Fuzzy Processor Architecture 198 3. Software Development Tool 200 4. Pipeline Subdivision 201 5. Layout Design Guidelines 202 6. Conclusions 204 References 204

Chapter 10 Designing a Simple System to Greatly Accelerate the Learning Speed of a Large Class of Fuzzy Learning Methods

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197

Marco Russo 207

1. Introduction 208 2. Fuzzy Logic 209

2.1 Fuzzy sets 209 2.2 Fuzzy reasoning 209 2.3 Fuzzification and defuzzification 211

3. A Brief Overview of the Main Fields Which Can Gain Greatly by Using the Accelerator Card Proposed 213 3.1 Genetic based systems 214 3.2 Neuro-fuzzy systems 214 3.3 Downhill simplex method 215

4. Description of the Card 215 5. General Evaluation of the Performance of the System

Proposed on FuGeNeSys 217 6. Enhancements 219 7. Architectural Organization of the Computer-Card System 220

7.1 RAM and local bus size 222 7.2 Master bus speed calculation 223

8. Learning Time Assessment 224 8.1 Fuzzy processor with several inputs 224 8.2 The normalized learning time 225


Chapter 11 Fuzzy Controller Synthesis Method Jean-Pierre Deschamps

1. Introduction 232 2. Fuzzy Control Algorithm 233

231

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3. Circuit Architecture 235 3.1 General structure 236 3.2 Synchronization 238 3.3 Look-up tables 239 3.4 Register bank 240 3.5 Arithmetic and logic unit (ALU) 241 3.6 Output ports 246

4. Synthesis Tools 247 4.1 Input language 247 4.2 Computation scheme generator 248 4.3 Computation scheme transformation 249 4.4 Program generator 250 4.5 Microprogram generator 251 4.6 Editors and loaders 252

5. Example 252 6. Division Algorithm 253 References 254

Chapter 12 Fuzzy Hardware Based on Encoded Trapezoids Antonio Ruiz, Julio Gutierrez, and J.A. Felipe Fernandez 257

1. Introduction 258 2. Fuzzy Sets and Inference Models 259

2.1 Fuzzy sets representation and encoding 259 2.2 Parametrized model of fuzzy inference rules 261

3. Two Levels of Abstraction in the Operation with Fuzzy Sets 264

4. Architectures for Making Fuzzy Inference at the Level of Fuzzy Set 264 4.1 Antecedents 265 4.2 Consequents 268 4.3 Description model 271

5. Calculation of Consequents by Product-Addition Operators 272

6. Comparison Between Methods for the Consequent 274 7. Conclusions 278 References 278

Chapter 13 Pulse Stream Techniques for Fuzzy Hardware Francisco Colodro Ruiz, Antonio J. Torralba Silgado, John Tombs, and Leopoldo Garcia Franquelo 283

1. Introduction 284

2. Architecture of the Fuzzy Controller 284 3. A Fuzzy Controller Using PWM Techniques 285

3.1 The defuzzifier 286 4. A Fuzzy Controller Using Stochastic Logic 288

4.1 The defuzzifier 288 4.2 On-chip learning 289

5. Conclusions and Future Research 292 References 292

Chapter 14 Fuzzy Cellular System: Characteristics and Architecture Riccardo Caponetto, Mario Lavorgna, Luigi Occhipinti,

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and GianGuido Rizzotto· 295

1. Introduction 296 2. The Cellular Fuzzy System Approach 296 3. Cellular Fuzzy Systems As Universal Computing

Machines 298 4. Digital Hardware Implementation 301 5. Image Processing Applications 303

5.1 Corrupted images filtering 303 5.2 Connected components detection 307


Chapter 15 Fuzzy Wavelets for Feature Extraction and Failure Classification

George Vachtsevanos, Vipin K Ramani, and Muid Mufti 311

1. Introduction 312 2. Architecture of An Intelligent Identification Algorithm 313

2.1 Pre-processing 313 2.2 Feature extraction 313 2.3 Fuzzification 315 2.4 Inferencing 315 2.5 Learning 315 2.6 Fault declaration 316

3. Review of Fuzzy Tools for Classification 316 3.1 Fuzzy algebraic concepts 316 3.2 Fuzzy inference engine 317 3.3 Fuzzy measures 320

4. The Entropy Concept 321 5. Wavelet Transforms 322

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5.1 Wavelet analysis 323 6. Fuzzy Wavelet Analysis 326

6.1 Fuzzification 328 7. Fuzzy Inferencing 329

7.1 Performance metrics 330 8. Detectability and Identifiability Measures 332

8.1 Identifiability as a special case of fuzzy entropy 333 9. Learning 334 10. On-Line Learning 334 11. Off-Line Learning 335

11.1 Optimization of rule-base via detectability and identifiability 335

12.DSP 337 12.1 Control module 338 12.2 Detector module 340 12.3 Dual memory access· 341

13. Examples and Results 342 13.1 Inspection of textile fabrics using FWA 342 13.2 Experimental setup 342 13.3 Technical approach 346


Chapter 16 A Building Block Approach to The Design of Analog Neuro-Fuzzy Systems in CMOS Digital Technologies Fernando Vidal-Verdu, Manuel Delgado-Restituto, Rafael Navas-Gonzalez, and Angel Rodriguez-Vazquez 357

1. Introduction 358 2. Singleton Fuzzy Inference System Architecture 359 3. CMOS Current-Mode Fixed-Function Nodes 362

3.1 Multidimensional minimum (layer 2) 362 3.2 Normalization circuit (layer 3) 364

4. Building Component of Adaptive Nodes 366 4.1 General considerations 366 4.2 Compound MOS transistors 367 4.3 Series transistor 368 4.4 Parallel transistor 369 4.5 Implementation ofB 370 4.6 Comparison 371

5. CMOS Membership Function Blocks 373 5.1 Singleton weighting 377

6. Hardware Compatible Learning 378 7. Interfaces Among Building Blocks 381

7.1 Interface to membership function circuitry 381 7.2 Interface between maximum and normalization

circuits 382

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7.3 Interface between normalization and singleton weighting circuits 382

8. Results 383 8.1 Chip demonstrators 383 8.2 Hardware-compatible learning 386


Chapter 17 Electronic Implementation of Complex Controllers Alfredo Sanz and Jorge Falco 391

1. Introduction 392 2. Autonomous Response System 393 3. Object Implementation 393 4. EDA Language 395 5. IDEA Tool 396 6. Experimental Robot 397 7. Fuzzy Logic Controllers 398 8. Analog Implementation 401 9. Fuzzification Interface 401 10. Decision-Making Unit 405 11. Defuzzification Interface 405 12. Conclusions 405 References 406

CONTRIBUTORS

INDEX

409

419

PREFACE

Fuzzy hardware developments have been a major force driving the applications of fuzzy set theory and fuzzy logic in both science and engineering. The fuzzy boom in Japan, as well as in other parts of the world, has generated a host of products and techniques demonstrating superior performance to conventional products. It is precisely that superior performance that has enhanced the scientific label, as well as the commercial label, of fuzzy set theory.

An important research trend is the design of improved fuzzy hardware. Recent investigations in the literature have shown increasing interest in both analog and digital implementations of fuzzy controllers in particular and fuzzy systems in general. Specialized analog and digital VLSI implementations of fuzzy systems, in the form of dedicated architectures, aim at the highest implementation efficiency. This particular efficiency is asserted in terms of processing speed and silicon utilization. Processing speed in particular has caught the attention of developers of fuzzy hardware and researchers in the field.

This edited volume of fuzzy hardware architectures and applications provides the reader with a comprehensive up-to-date look at recent works describing new innovative developments of fuzzy hardware. The contributors are widely known for their research in fuzzy hardware and have acquired international visibility working and publishing in this field.

Lotfi A. Zadeh introduced the concept ofjuzzy sets in 1965. In 1974, E. H. Mamdani developed the first fuzzy inference procedure. This was the starting point for a dramatic proliferation of fuzzy applications. Yamakawa and Watanabe were the first to propose hardware implementations of fuzzy logic controllers in analog and digital

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techniques, respectively. Consequently, fuzzy hardware implementations started to get increased attention on the part of researchers, resulting in tremendous evolution of fuzzy hardware in the last two decades. Chapter 1 presents an overview of fuzzy hardware systems, covering both analog and digital issues. In Chapter 2, the authors present an overview of the activities pertaining to the development of three generations of fuzzy hardware in analog technique at the German National Research Center for Information Technology, System Design Technology Institute. Mainly highlighting the novelty of each development stage, the chapter concludes with the exploration of applications areas for the presented chip developments.

Chapter 3 presents a reconfigurable fuzzy neuron (RFN) for implementing both aggregative (OR, AND) and referential (matching, difference, dominance, and inclusion) operations. The RFN is composed of three main units: reconfigurable fuzzy processor (RFP), learning unit (LU), and local memory unit (MU). The architecture combines both structural and parametric flexibility in the design of a network of fuzzy neurons. In-situ learning, using a fuzzy back propagation learning algorithm, is used to provide the parametric flexibility. This flexibility encompasses both the neural interconnections and reference parameter points.

In recent years, the number of ASIC designs which include fuzzy or neural controllers has increased. The basic structure of these controllers is usually repeated and, therefore, it seems logical to create a tool that automates the development of these controllers and allow the engineer to concentrate on the more specific aspects of the design under development. Chapter 4 presents the results obtained with AFAN, a software tool designed to generate analog or digital implementations of fuzzy and neural controllers from a set of specifications. For digital design, AF AN accounts for different aspects related to the size of the circuit (i.e., arithmetic resolution, number of inputs and outputs, number of rules or number of neurons per layer, etc.), and the speed-area trade-off is taken into account in the selection of the internal architecture. The result is a file containing the VHDL code of a directly synthesizable fuzzy or neural controller. For analog designs, AF AN uses a library of standard cells and results in a file with the structural description of the analog circuit whose layout is obtained using Cadence software.

In Chapter 5, the authors propose a general-purpose silicon compiler for the development of fuzzy, as well as neuro-fuzzy, hardware systems. High level synthesis of analog fuzzy hardware systems is achieved by translating fuzzy linguistic descriptions into hardware description directives in terms of the relationships of generic LR fuzzy cells. Chip layout of target systems can be automatically generated by regarding the generic LR fuzzy cells as standard cells in existing EDA tools. The LR fuzzy cell library adopts CMOS analog current-mode technology to achieve advantages of high performance, low power, and small chip area. Examples of singleton, non-singleton fuzzy controller and fuzzy neural network with different forms of membership functions, fuzzy rules and inference methods are illustrated and evaluated. Evaluations show that the fuzzy systems synthesized by the proposed silicon compilation procedure inherit the advantages of the generic LR fuzzy cells.

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Fuzzy modeling works by means of extracting a large amount of information from the system dealt with. All these data are crossed with the occurrences of the input variables to obtain good results. To be competitive, this process must be carried out efficiently, without restrictions on the model and by saving resources. Efficiency requires application-specific solutions, hardware implementations, and massive parallelism, whereas fuzzy universal machines must be employed to avoid restrictions. The serial data flow design presented in Chapter 6 allows to build fast and compact circuits due to the implementation of small processing units and narrow data paths. Inside the serial architectures, the most-significant-digitlbit-frrst data flow is better suited for the implementation of several fuzzy operators. Therefore, the most interesting processing units to be implemented in an efficient fuzzy processor are hardware designs based on on-line fuzzy algorithms. The design of such circuits in the implementation of a fuzzy microprocessor is described in this chapter.

Chapter 7 proposes a methodology for automatic generation of digital hardware implementations of piecewise-linear fuzzy systems. The methodology allows the user to tailor the hardware on the specific application by selecting how much memory will be devoted to the storage of intermediate results. This is done by adopting the concept of piecewise-linear fuzzy systems and by a novel hardware architecture. For an n-input fuzzy system with m fuzzy domains on each input axis, mn to 2n-1 mn words can be allocated to obtain a throughput ranging from one inference every 2n memory read cycles (which is a lower bound for conventional implementations) to n+ I memory read cycles. Specifications from the user drive the automatic generation of the VHDL description of the hardware architecture, and synthesis tools compile the VHDL code to hardware on the desired technology.

Chapter 8 considers the design of a dedicated VLSI fuzzy processor for fuzzy applications. An analysis of inference techniques and their complexity has led to the definition of an inference execution model which optimizes processing times. Its main features are: parallel processing of several fuzzy rules, pre-computation of the degree of positive truth of the antecedents, computation of the degree of truth of the only active rules, and optimized representation of membership functions. The processor was synthesized using HCMOS5 as target technology, resulting in processing speed of up to 2.5 MFLIPS (256 rules, 8 antecedents, 1 consequent) and estimated silicon area of 30 mm2.

In Chapter 9, the authors describe the architecture of a very small size high-speed fuzzy chip with two inputs and one output. Input data set rate of 80 ns is obtained by means of 4 clock pipeline cycles synchronized with a 50 MHz signal, and the chip architecture processes only the significant fuzzy rules by means of a parallel pipeline structure. The design uses VHDL language as front-end tool and CAD layout placement and routing utilities as back-end tools. Using cell-based digital 0.7 f.lm CMOS ES2 technology library, the VHDL synthesis and layout design produced a chip area of about 12 mm2.

The use of fuzzy logic in applications in which learning time is the major prerequisite is the motivation behind the design of the multiprocessor card, that can

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significantly accelerate the learning process of fuzzy inferences, considered in Chapter 10. The card is completely general and works well with any learning technique (e.g., evolutionary algorithms, weight perturbation method, downhill simplex method, and so on) in which the learning time is mostly due to learning error calculations.

Chapter 11 is concerned with the implementation of fuzzy controllers by means of specific components. A first solution consists of using classical high level synthesis tools based on scheduling and hardware allocation algorithms, and a logic synthesis tool. However, the results obtained for low performance controllers (not many inference rules and relatively low throughput) are rather disappointing and, therefore, a more specific methodology is chosen and demonstrated to be an efficient one. This work is part of a more ambitious project aimed at defining and developing efficient methods for designing embedded systems. In this first phase of the project, a complete methodology, along with the corresponding design tools, has been developed within the following restricted framework: circuits made up of a parameterized data path and a control unit that execute a branchless microprogram. The data path design amounts to the instantiation and interconnection of several VHDL-described parameterized blocks and compiled macrocells. The control unit includes phase generator, microinstruction counter and microprogram memory (compiled ROM), and its design amounts practically to the generation of the contents of the microprogram memory. The set of tools developed to make the microprogram generation easy and complemented by two front-end specific programs (input language translator and lattice optimization algorithm) were tested on several fuzzy controller designs.

In Chapter 12, the authors present a new design method for fuzzy controller architectures, based on the representation of membership functions as trapezoids and on the calculus of operations using only the four parameters that encode a trapezoid. This is a strategic alternative to the classical operation with individual membership degrees by sweeping the universe of discourse and operating element by element. The approach determines two abstraction levels: fuzzy set and domain element. It is shown that the operation at the fuzzy set level has advantages in terms of performance and cost. To this end, the structural models of both types of fuzzy controllers are compared at the level of register transfer (RT). This strategy can be applied not only to the design of architectures for fuzzy controllers but also to any system that can operate with membership functions.

Pulse stream techniques represent a different approach to hardware design of fuzzy systems. Two pulse stream techniques, used to implement fuzzy controllers, are presented in Chapter 13. In pulse width modulation (PWM), a signal is represented by means of a pulse whose duration is proportional to its value, and in stochastic logic (SL), a signal is represented by a pulse stream that generates pulses with a probability proportional to the instantaneous value of the signal. The authors discuss the rationale behind both techniques and present some actual implementations of fuzzy controllers.

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A new family of discrete time nonlinear dynamic systems is introduced in Chapter 14. The basic elements of these systems are called cells; the cells are identical, they can be thought of as nodes in a rectangular grid, and they interact with their neighboring cells similarly to cellular neural networks. With this new architecture, more general behavior is obtained by using two sets of fuzzy logic rules: the fIrst set is governing the local interactions between adjacent cells while the second set is governing the dynamic evolution of the cell itself. In fact, the combination of these two sets allows a dynamic evolution of the global cellular system, enabling it to implement several image processing operations, locally described in a linguistic way, and complex dynamics simulation such as the implementation of reaction-diffusion equations for pattern formation, slow-fast dynamic systems, spiral waves generation, cellular automata, etc. It is shown that fuzzy cellular systems are general enough to implement the "game of life" and are therefore equivalent to a Turing machine. The authors propose a scheme of the hardware architecture of the single fuzzy cellular system, and describe the single elements of the basic cell and outline its intrinsic structure. Also reported are results pertaining to the application of fuzzy cellular systems to some image processing tasks such as noise removal from corrupted digital images (both gray scale and color images) and connected components detection.

A new method is proposed in Chapter 15 for feature extraction and failure classifIcation in complex systems. The technique of fuzzy wavelet analysis is introduced which uses fuzzifIed wavelet transform to analyze wide bandwidth features. A special attribute of this tool is its ability to employ localized time/frequency analysis of fuzzy data for feature extraction and eventual failure classifIcation purposes. Performance measures of detectability and identifIability are dermed to assist in assessing the performance of the algorithm. Performance improvement is achieved through a learning mechanism based on the detectability and identifIability measures. A fuzzy similarity measure is also introduced to reduce sensitivity to noise. The algorithm uses both on-line and off-line learning for designing and updating the rule base. An example is discussed in the area of fabric defect detection and identifIcation applying the fuzzy wavelet analysis technique. Experimental data indicate the robustness and effectiveness of the proposed algorithms. Finally, a hardware implementation method is proposed utilizing a DSPbased multi-tasking and multi-processing platform that accommodates speed of response in a cost-effective way.

Chapter 16 presents adaptive circuit blocks and related learning algorithms to design neuro-fuzzy inference systems using analog integrated circuits in CMOS standard VLSI technologies. The proposed circuit building blocks are arranged in an architecture composed of fIve layers: fuzzifIcation, T-norm, normalization, consequent, and output. Inference is performed using Takagi and Sugeno's If-Then rules, particularly where the rule's output contains only a constant term - a singleton. The proposed learning scheme uses weight perturbation for the fuzzifIcation layer and outstar for the output layer. Measurements from two chips are presented for demonstration purposes, both in CMOS single-poly, double-metal technologies. The fIrst has three-input, four rules and obtains operation speed in the range of 5 MFlips

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with around 1 % systematic errors. The other is capable of evaluating 16 programmable rules at a speed of 2.5 MFlips (2.5x106 fuzzy inferences per second) with 8.6 m W power consumption. It includes also on-chip digital control and memory circuitry for programmability. Thus, the chip parameters can be learned in situ, for operation in a changing environment, by using the devised hardwarecompatible learning algorithms.

The autonomous response system paradigm is developed in Chapter 17 to design complex fuzzy controllers together with a method for their implementation with analog electronic circuits. The fuzzy controller can be designed using operational amplifiers to implement the fuzzy If-Then rules and the set of membership functions characterizing the linguistic terms associated with the inputs and outputs of the fuzzy controller.

Many individuals deserve recognition for making this volume become a reality. First and foremost, the contributors to this book for their effort, time, and promptness. We all had to work under a somewhat stringent time table. We are also grateful to Alex Greene and the Kluwer Academic Publishers staff for their advice and commitment to this project. Editing this volume would not have been possible without the encouragement and support of Professor Uri Shaked, Dean of the Faculty of Engineering at Tel-Aviv University and Professor Michael Kovac, Dean of the College of Engineering at the University of South Florida, and we dedicate the book to both of them.

We hope this book will serve as an impetus for continued research and development ofJuzzy hardware architectures and applications.

Tel-Aviv, 1997

Abraham Kandel Gideon Langholz

About the Editors

Abraham Kandel is Professor and Endowed Eminent Scholar in Computer Science and Engineering, and the Chairman of the Department of Computer Science and Engineering at the University of South Florida. Previously he held the position of Professor and Chairman of the Computer Science Department at Florida State University as well as the Director of the Institute of Expert Systems and Robotics at FSU and the Director of the Florida State University System Center for Artificial Intelligence. He is a Fellow of the IEEE, Fellow of the American Association for the Advancement of Science, and Fellow of the New York Academy of Sciences.

Dr. Kandel is a member of the editorial boards of various international journals including Fuzzy Sets and Systems, IEEE Transactions on System, Man and Cybernetics, IEEE Transactions on Fuzzy Systems, IEEE Micro, Iriformation Sciences, and Engineering Applications of Artificial Intelligence. He has written over 350 research papers for numerous professional publications in computer science and engineering, as well as authored, co-authored, edited, and co-edited 23 books mostly in the area of applied fuzzy logic. At the University of South Florida, Dr. Kandel received the College of Engineering Outstanding Research Award in 1993/4, the University's Ashford Distinguished Scholar Award in 1995, and the Sigma-Xi Outstanding Faculty Researcher Award in 1995. He also received the MOISIL International Foundation Gold Medal for lifetime achievement in the area of Artificial Intelligence in 1996, and the State of Florida PEP Award in 1997.

Gideon Langholz is Professor of Electrical Engineering in the Department of Electrical Engineering-Systems at Tel-Aviv University. He was Chairman of the Department of Electrical Engineering-Systems at Tel-Aviv University, and held various academic positions at the University of London, the Univers'ity of California at Santa Barbara, and Florida State University.

Dr. Langholz is a Senior Member of the IEEE and a member of the editorial board of the international journal Engineering Applications of Artificial Intelligence. He has written over 70 research papers for numerous professional publications in electrical and computer engineering. He is co-author of Digital Logic Design (1988), Elements of Computer Organization (1989), and Fuzzy Expert System Tools (1996), and coeditor of Hybrid Architectures for Intelligent Systems (1992) and Fuzzy Control Systems (1994). His research interests include artificial intelligence, fuzzy systems, neural networks, genetic algorithms, learning automata, telecommunication networks, routing and flow control.

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