Fuzzy Logic with Engineering Applications E-Book

Timothy J. Ross

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 949

Veröffentlichungsjahr: 2016

Beschreibung

The latest update on this popular textbook

The importance of concepts and methods based on fuzzy logic and fuzzy set theory has been rapidly growing since the early 1990s and all the indications are that this trend will continue in the foreseeable future. Fuzzy Logic with Engineering Applications, Fourth Edition is a new edition of the popular textbook with 15% of new and updated material. Updates have been made to most of the chapters and each chapter now includes new end-of-chapter problems.

Key features:

• New edition of the popular textbook with 15% of new and updated material.
• Includes new examples and end-of-chapter problems.
• Has been made more concise with the removal of out of date material.
• Covers applications of fuzzy logic to engineering and science.
• Accompanied by a website hosting a solutions manual and software.

The book is essential reading for graduates and senior undergraduate students in civil, chemical, mechanical and electrical engineering as wells as researchers and practitioners working with fuzzy logic in industry.

Leseprobe

FUZZY LOGIC WITH ENGINEERING APPLICATIONS

Fourth Edition

Timothy J. Ross

University of New Mexico, USA

This edition first published 2017© 2017 John Wiley & Sons, Ltd.

First edition published 1995Second edition published 2004Third edition published in 2010

Registered OfficeJohn Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

Library of Congress Cataloging‐in‐Publication Data

Names: Ross, Timothy J., author.Title: Fuzzy logic with engineering applications / Timothy J. Ross.Description: Fourth edition. | Southern Gate, Chichester, West Sussex, United Kingdom : John Wiley & Sons Inc., 2017. | Includes bibliographical references and index.Identifiers: LCCN 2016021917 | ISBN 9781119235866 (pbk.) | ISBN 9781119235859 (Adobe PDF) | ISBN 9781119235842 (epub)Subjects: LCSH: Engineering--Statistical methods. | Fuzzy logic.Classification: LCC TA340 .R673 2017 | DDC 620.001/511313--dc23 LC record available at https://lccn.loc.gov/2016021917

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

This book is dedicated to the memory of my loving mother, Phyllis; to my dear aunts, Glee, Ruth, and Virginia; and to my beloved cousin, Carol, all of whom have departed in the last five years; and to my partner, Laura, who is giving me much optimism for the future. And, to my dear US/Brazilian friends, Cassiano and Kenya, for their unconditional friendship since 2010. Finally, to my new grandson, Jackson, I give you my best wishes in life.

About the Author

Timothy J. Ross is Professor and Regents’ Lecturer of Civil Engineering at the University of New Mexico. He received his PhD in Civil Engineering from Stanford University, his MS from Rice University, and his BS from Washington State University. Professor Ross has held previous positions as Senior Research Structural Engineer, Air Force Weapons Laboratory, from 1978 to 1986; and Vulnerability Engineer, Defense Intelligence Agency, from 1973 to 1978. Professor Ross has authored more than 150 publications and has been active in the research and teaching of fuzzy logic since 1983. He is the founding Co‐Editor‐in‐Chief of the International Journal of Intelligent and Fuzzy Systems, the co‐editor of Fuzzy Logic and Control: Software and Hardware Applications, and the co‐editor of Fuzzy Logic and Probability Applications: Bridging the Gap. His sabbatical leaves in 1994–1995 at the US Army Environmental Policy Institute, Atlanta, Georgia; in 2001–2002 at the University of Calgary, Alberta, Canada; in 2008–2009 at Gonzaga University in Spokane, Washington; and most recently in 2015 at the Air Force Research Laboratory at Kirtland AFB, New Mexico, have resulted in the education of numerous additional students, faculty, and research professionals in the subject of fuzzy logic because he transferred this technology to all of these institutions. Ross continues to be active in applying fuzzy logic in his areas of research: decision support systems, reliability theory, data fusion, and structural engineering.

Preface to the Fourth Edition

My primary motivations for writing the fourth edition of this text have been to (1) reduce the length of the text, (2) correct the errata discovered since the publication of the third edition, and (3) introduce limited new material for the readers. The first motivation has been accomplished by eliminating some sections that are rarely taught in the classroom by various faculty using this text and by eliminating some sections that do not add to the utility of the text as a tool to learn basic fundamentals of the subject.

Since the first edition was published, in 1995, the technology of fuzzy set theory and its application to systems, using fuzzy logic, has moved rapidly. Developments in other theories such as possibility theory and evidence theory (both being elements of a larger collection of methods under the rubric “generalized information theories”) have shed more light on the real virtues of fuzzy logic applications, and some developments in machine computation have made certain features of fuzzy logic much more useful than in the past. In fact, it would be fair to state that some developments in fuzzy systems are quite competitive with other, linear algebra‐based methods in terms of computational speed and associated accuracy.

There is some new material which is included in the fourth edition to try to capture some of the newer developments; the keyword here is some because it would be impossible to summarize or illustrate even a small fraction of the new developments of the last six years since the third edition was published. As with any book containing technical material, the third edition contained errata that have been corrected in this fourth edition. As with the first three editions, a solutions manual for all problems in the fourth edition and software can be obtained by qualified instructors who visit www.wiley.com/go/ross/fuzzy4e and provide official documentation of their teaching status. In addition to the solutions manual, a directory of software will be made available to all student users and faculty of the text on this same website. Most of the software routines make use of the MATLAB platform, and most of the routines have been written by my students, except for the standard routines that exist as MATLAB functions.

As I discussed in the preface of the third edition, the axioms of a probability theory referred to as the excluded middle are again referred to in this edition as axioms—never as laws. The operations due to De Morgan are also not referred to as laws, but as principles because these principles do apply to some (not all) uncertainty theories (e.g., probability and fuzzy). The excluded middle axiom (and its dual, the axiom of contradiction) are not laws; Newton produced laws, Kepler produced laws, Darcy, Boyle, Ohm, Kirchhoff, Bernoulli, and many others too numerous to list here all developed laws. Laws are mathematical expressions describing the immutable realizations of nature. Definitions, theorems, and axioms collectively can describe a certain axiomatic foundation describing a particular kind of theory, and nothing more; in this case, the excluded middle and other axioms can be used to describe a probability theory. Hence, if a fuzzy set theory does not happen to be constrained by an excluded middle axiom, it is not a violation of some immutable law of nature like Newton’s laws; fuzzy set theory simply does not happen to have an axiom of the excluded middle; it does not need, nor is constrained by, such an axiom. In fact, as early as 1905 the famous mathematician L. E. J. Brouwer defined this excluded middle axiom as a principle in his writings; he showed that the principle of the excluded middle was inappropriate in some logics, including his own, which he termed intuitionism. Brouwer observed that Aristotelian logic is only a part of mathematics, the special kind of mathematical thought obtained if one restricts oneself to relations of the whole and part. Brouwer had to specify in which sense the principles of logic could be considered “laws” because within his intuitionistic framework thought did not follow any rules, and, hence, “law” could no longer mean “rule” (see the detailed discussions on this in Chapters 5 and 13). In this regard, I continue to take on the cause advocated by Brouwer more than a century ago.

Also in this fourth edition, as in previous editions, I do not refer to “fuzzy measure theory” but instead describe it as “monotone measure theory”; the reader will see this in the title of Chapter 13. The former phrase still causes confusion when referring to fuzzy set theory; we hope to help in ending this confusion. In Chapter 13, in describing the monotone measure, m, I use the phrase describing this measure as a “basic evidence assignment (bea),” as opposed to the early use of the phrase “basic probability assignment (bpa).” Again, we attempt to avoid confusion with any of the terms typically used in probability theory.

As with the first three editions, this fourth edition is designed for the professional and academic audience interested primarily in applications of fuzzy logic in engineering and technology. I have found that the majority of students and practicing professionals are interested in the applications of fuzzy logic to their particular fields. Hence, the text is written for an audience primarily at the senior undergraduate and first‐year graduate levels. With numerous examples throughout, this text is written to assist the learning process of a broad cross section of technical disciplines. It is primarily focused on applications, but each of the chapters begin with the rudimentary structure of the underlying mathematics required for a fundamental understanding of the methods illustrated.

Chapter 1 introduces the basic concept of fuzziness and distinguishes fuzzy uncertainty from other forms of uncertainty. It also introduces the fundamental idea of set membership, thereby laying the foundation for all material that follows, and presents membership functions as the format used for expressing set membership. The chapter summarizes a historical review of uncertainty theories and reviews the idea of “sets as points” in an n‐dimensional Euclidean space as a graphical analog in understanding the relationship between classical (crisp) and fuzzy sets. A new section in the chapter addresses the intuition of propagating uncertainty by showing an example that compares the results of propagating probabilities on the one hand, or membership values on the other, through a simple nonlinear function. In this example there are some counterintuitive findings that readers will find both interesting and instructive.

Chapter 2 reviews classical set theory and develops the basic ideas of fuzzy sets. Operations, axioms, and properties of fuzzy sets are introduced by way of comparisons with the same entities for classical sets. Various normative measures to model fuzzy intersections (t‐norms) and fuzzy unions (t‐conorms) are summarized.

Chapter 3 develops the ideas of fuzzy relations as a means of mapping fuzziness from one universe to another. Various forms of the composition operation for relations are presented. Again, the epistemological approach in this chapter uses comparisons with classical relations in developing and illustrating fuzzy relations. Chapter 3 also illustrates methods to determine the numerical values contained within a specific class of fuzzy relations, called similarity relations. The section on a three‐dimensional physical analogy of equivalence relations has been deleted.

Chapter 4 discusses the fuzzification of scalar variables and the defuzzification of membership functions. It introduces the basic features of a membership function and it discusses, briefly, the notion of interval‐valued fuzzy sets. Defuzzification is necessary in dealing with the ubiquitous crisp (binary) world around us. The chapter details defuzzification of fuzzy sets and fuzzy relations into crisp sets and crisp relations, respectively, using lambda‐cuts, and it describes a variety of methods to defuzzify membership functions into scalar values. Some of the defuzzification methods in the third edition have been deleted because they are seldom used in practice and because they are covered elsewhere in the literature. Examples of all methods are given in the chapter.

Chapter 5 introduces the precepts of fuzzy logic, again through a review of the relevant features of classical, or a propositional, logic. Various logical connectives and operations are illustrated. There is a thorough discussion of the various forms of the implication operation and the composition operation provided in this chapter. Three different inference methods, popular in the literature, are illustrated. Approximate reasoning, or reasoning under imprecise (fuzzy) information, is also introduced in this chapter. Basic IF–THEN rule structures are introduced and three graphical methods of inference are presented. The section on Natural Language has been shortened. A few more examples of the difficulties of using the axiom of the excluded middle are given in the summary of the chapter.

Chapter 6 provides several classical methods of developing membership functions, including methods that make use of the technologies of neural networks, genetic algorithms, and inductive reasoning.

Chapter 7 presents six automated methods that can be used to generate rules and membership functions from observed or measured input–output data. The procedures are essentially computational methods of learning. Examples are provided to illustrate each method. Many of the problems at the end of the chapter will require software; this software can be downloaded from www.wiley.com/go/ross/fuzzy4e.

Beginning the second category of chapters in the book highlighting applications, Chapter 8 continues with the rule‐based format to introduce fuzzy nonlinear simulation and complex system modeling. In this context, nonlinear functions are seen as mappings of information “patches” from the input space to information “patches” of the output space, instead of the “point‐to‐point” idea taught in classical engineering courses. Fidelity of the simulation is illustrated with standard functions, but the power of the idea can be seen in systems too complex for an algorithmic description. This chapter formalizes fuzzy associative memories (FAMs) as generalized mappings.

Chapter 9 develops fuzzy decision making by introducing some simple concepts in ordering, preference and consensus, and multiobjective decisions. It introduces the powerful concept of Bayesian decision methods by fuzzifying this classic probabilistic approach. This chapter illustrates the power of combining fuzzy set theory with probability to handle random and nonrandom uncertainty in the decision‐making process.

Chapter 10 discusses a few fuzzy classification methods by contrasting them with classical methods of classification and develops a simple metric to assess the goodness of the classification, or misclassification. This chapter also summarizes classification using equivalence relations. It now has a section on pattern recognition, gleaned from the third edition. This section introduces a useful metric in pattern recognition using the algebra of fuzzy vectors. A single‐feature and a multiple‐feature procedure are summarized in the chapter. The section on image processing has been deleted because other books have extensive coverage of this area.

The chapter in the third edition on fuzzy arithmetic and fuzzy numbers has been deleted. A summary of Zadeh’s extension principle and a few simple examples of fuzzy arithmetic are included in Chapter 12.

Chapter 11 introduces the field of fuzzy control systems. A brief review of control system design and control surfaces is provided. Simple example problems in control are provided. Two sections in this chapter are worth noting: fuzzy engineering process control and fuzzy statistical process control, with examples on both provided. A discussion of the comparison of fuzzy and classical control is contained in the chapter summary, and a few more examples of fuzzy control in industrial systems and applications are also included.

Chapter 12 has been extensively changed by including more information on genetically evolved fuzzy cognitive maps, and new sections on the extension principle and fuzzy arithmetic and on fuzzy data fusion are also detailed. Previous sections on fuzzy optimization and fuzzy agent‐based methods are still contained in this chapter.

Finally, Chapter 13 enlarges the reader’s understanding of the relationship between fuzzy uncertainty and random uncertainty (and other general forms of uncertainty, for that matter) by illustrating the foundations of monotone measures. The chapter discusses monotone measures in the context of evidence theory, possibility theory, and probability theory. The chapter has a section on methods to develop approximate possibility distribution functions derived from both data intervals and scalar point data.

Most of the text can be covered in a one‐semester course at the senior undergraduate level. In fact, most science disciplines and virtually all math and engineering disciplines contain the basic ideas of set theory, mathematics, and deductive logic, which form the only knowledge necessary for a complete understanding of the text. For an introductory class, instructors may want to exclude some or all of the material covered in the last section of Chapter 6 (neural networks, genetic algorithms, and inductive reasoning), Chapter 7 (automated methods of generation), and any of the final three chapters: Chapter 11 (fuzzy control), Chapter 12 (miscellaneous fuzzy applications), and Chapter 13 on alternative measures of uncertainty. I consider the applications in Chapter 8 on simulations, Chapter 9 on decision making, and Chapter 10 on classification to be important in the first course on this subject. The other topics could be used either as introductory material for a graduate‐level course or for additional coverage for graduate students taking the undergraduate course for graduate credit.

In terms of organization, the first eight chapters of the text develop the foundational material necessary to get students in a position where they can generate their own fuzzy systems. The last five chapters use the foundation material from the first eight chapters to present specific applications.

Most of the problems at the end of each chapter have been revised with different numbers, and there are many new problems that have been added to the text and some problems from the third edition deleted. In reducing the length of the book, some old problems have been deleted from many chapters. The problems in this text are typically based on current and potential applications, case studies, and education in intelligent and fuzzy systems in engineering and related technical fields. The problems address the disciplines of computer science, electrical engineering, manufacturing engineering, industrial engineering, chemical engineering, petroleum engineering, mechanical engineering, civil engineering, environmental engineering, and engineering management, and a few related fields such as mathematics, medicine, operations research, technology management, the hard and soft sciences, and some technical business issues. The references cited in the chapters are listed toward the end of each chapter. These references provide sufficient detail for those readers interested in learning more about particular applications using fuzzy sets or fuzzy logic. The large number of problems provided in the text at the end of each chapter allows instructors a sizable problem base to afford instruction using this text on a multisemester or multiyear basis, without having to assign the same problems term after term.

Again I wish to give credit to some of the individuals who have shaped my thinking about this subject since the first edition of 1995, and to others who by their simple association with me have caused me to be more circumspect about the use of the material contained in the text. Three colleagues at Los Alamos National Laboratory have continued to work with me on applications of fuzzy set theory, fuzzy logic, and generalized uncertainty theory: Dr. Greg Chavez (who wrote much of Chapter 7) and Drs. Jamie Langenbrunner and Jane Booker (retired), who both have worked extensively in an area known as quantification of margins and uncertainty (QMU) in assessing reliability of man‐made systems; in this regard these three individuals have all explored the use of fuzzy logic and possibility theory in their work. I wish to acknowledge the organizational support of two individuals in the Brazilian Institute, Instituto de Pesquisas Engergéticas e Nucleares (IPEN), in São Paulo, Brazil. These two researchers, Drs. Francisco Lemos and Antônio Barroso, through their invitations and travel support, have enabled me to train numerous Brazilian scientists and engineers in fuzzy logic applications in their own fields of work, most notably nuclear waste management, knowledge management, and risk assessment. My discussions with them have given me ideas about where fuzzy logic can impact new fields of inquiry.

I wish to thank two of my recent graduate students who have undertaken MS theses or PhD dissertations related to fuzzy logic and whose diligent work has assisted me in writing this new edition: Clay Phillips, Sandia National Laboratory, and Donald Lincoln, NStone Corporation. These former students have helped me with additional material that I have added in Chapter 12 and have helped discover some errata in this text. There have been numerous students over the past five years who have found much of the errata I have corrected; unfortunately, too numerous to mention in this brief preface. I want to thank them all for their contributions.

Four individuals need specific mention because they have contributed some sections to this text. I would like to thank specifically Dr. Jerry Parkinson for his contributions to Chapter 11, in the areas of chemical process control and fuzzy statistical process control; Dr. Greg Chavez for his contributions in automated methods; Dr. Sunil Donald for his early work in possibility distributions in Chapter 13; and Dr. Jung Kim for his contribution in Chapter 13 of a new procedure to combine disparate interval data. I would like to acknowledge the work of two graduate students at the University of New Mexico: Rashid Ahmad who has helped in developing some equations and figures for one chapter in the text, and to Pradeep Paudel for the development of the solutions manual for the text.

One individual deserves my special thanks and praise, and that is Professor Mahmoud Taha, my colleague in Civil Engineering at the University of New Mexico. In the last five years he has continued with his work in fuzzy logic applications, pattern recognition, and applications using possibility theory; I am proud and grateful to have been his mentor. I am indebted to his collaborations, his quick adaptation in the application of these tools, and in being a proficient research colleague of mine.