MTH645 Handouts Complete

This edition first published 2010 © 2010 John Wiley & Sons, Ltd

First edition published 1995

Second edition published 2004

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Library of Congress Cataloging-in-Publication Data Ross, Timothy J. Fuzzy logic with engineering applications / Timothy J. Ross.–3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-74376-8 (cloth)

1. Engineering mathematics. 2. Fuzzy logic. I. Title.

TA331.R74 2010

620. 001′511313–dc22 2009033736

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

ISBN: 978-0-470-74376-8

Set in 10/12pt Times Roman by Laserwords Pvt Ltd, Chennai, India Printed in Singapore by Fabulous Printers Pte Ltd This book is dedicated to my brother Larry, my cousin Vicki Ehlert and my best friends Rick and Judy Brake, all of whom have given me incredible support over the past 5 years. Thank you so much for helping me deal with all my angst!

CONTENTS

About the Author

xiii

Preface to the Third Edition

xv

1 Introduction

The Case for Imprecision A Historical Perspective The Utility of Fuzzy Systems Limitations of Fuzzy Systems The Illusion: Ignoring Uncertainty and Accuracy Uncertainty and Information The Unknown Fuzzy Sets and Membership Chance Versus Fuzziness Sets as Points in Hypercubes Summary References Problems

2 Classical Sets and Fuzzy Sets

Classical Sets Operations on Classical Sets Properties of Classical (Crisp) Sets Mapping of Classical Sets to Functions Fuzzy Sets Fuzzy Set Operations Properties of Fuzzy Sets Alternative Fuzzy Set Operations Summary References Problems