Liberty Mutual Exhibit 1021
`Liberty Mutual v. Progressive
`CBM2012-00002
`Page 00001
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`

`

`Library of Congress Cataloging-in-Publication Data
`
`Yen, John.
`Fuzzy logic: intelligence, control, and information
`John Yen and Reza Langari
`p,
`cm.
`Includes bibliographical references and index.
`ISBN: 0-13-525817-0
`1. Fuzzy logic. I. Langari, Reza. 11. Title.
`QA9.64 .Y46 1998
`511.3--dc21
`
`98-40882
`CIP
`
`Publisher: Tom Robbins
`Production editor: Edward DeFelippis
`Editor-in-chief: Marcia Horton
`Managing editor: Eileen Clark
`Assistant vice president of production and manufacturing: David W Riccardi
`Art director: Jayne Conte
`Cover designer: Bruce Kenselaar
`Manufacturing buyer: Pat Brown
`Editorial assistant: Dan DePasquale
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`
`
`.3?
`
`©1999 by Prentice-Hall, Inc.
`Simon & Schuster IA Viacom Company
`Upper Saddle River, New Jersey 07458
`
`All rights reserved. No part of this book may be
`reproduced, in any form or by any means,
`without permission in writing from the publisher.
`
`The author and publisher of this book have used flieir best efforts in preparing this book. These efforts include the
`development, research, and testing of the theories and programs to determine their effectiveness. The author and
`publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation
`contained in this book. The author and publisher shall not be liable in any event for incidental or consequential
`damages in connection with, or arising out of, the furnishing, performance, or use of these programs.
`Printed in the United States of America
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`7 6 5 4 3
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`2
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`ISBN 0-13-525817-0
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`Prentice—Hall International (UK) Limited. London
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`Page 00002
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`PART I
`
`FUZZY LOGIC
`
`Page 00003
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`

`INTRODUCTION
`
`After being mostly viewed as a controversial technology for two decades, fuzzy logic has
`finally been accepted as an emerging technology since the late 19803. This is largely due
`to a wide array of successful applications ranging from consumer products, to industrial
`process control, to automotive applications. Before we engage in an in-depth discussion of
`technical issues concerning fuzzy logic, however, we must first place this paradigm in per—
`spective. For this, we first clarify two meanings of the term “fuzzy logic” and present a
`brief history of the development of fuzzy logic technology and its applications. We will
`then discuss the insights that motivated the birth of this technology. This is followed by a
`clarification of some of the common misunderstandings about fuzzy logic.
`
`~
`
`1.1
`What Is Fuzzy Logic?
`
`The term fuzzy logic has been used in two different senses. It is thus important to clarify
`the distinctions between these two different usages of the term. In a narrow sense, fuzzy
`logic refers to a logical system that generalizes classical two-valued logic for reasoning
`under uncertainty. In a broad sense, fuzzy logic refers to all of the theories and technolo-
`gies that employ fuzzy sets, which are classes with unsharp- boundaries.
`For instance, the concept of “warm room temperature” may be expressed as an inter—
`val (e.g., [700 F, 78 o F]) in classical set theory. However, the concept does not have a well—
`defined natural boundary. A representation of the concept closer to human interpretation is
`to allow a gradual transition from “not warm” to “warm.” In order to achieve this, the
`notion of membership in a set needs to become a matter of degree. This is the essence of
`fuzzy sets. An example of a classical set and a fuzzy set is shown in Fig ll, where the ver—
`
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`
`
`
`
`
`
`1Chapter Introduction
`
`
`
`FIGURE 1.1
`
`A Classical Set and a Fuzzy Set Representation of “Warm Room Temperature”
`
`A Membership
`
`Membership
`
`
`
`0
`
`70
`
`78
`
`0
`
`‘ 70
`
`' 78
`
`T (OF)
`T (OF)
`The broad sense of fuzzy logic includes the narrow sense of fuzzy logic as a branch.
`Other areas include fuzzy control, fuzzy pattern recognition, fuzzy arithmetic, fuzzy math—
`ematical programming, fuzzy probability theory, fuzzy decision analysis, fuzzy neural net-
`works theory, and fuzzy topology, etc. In all these areas, a conventional black—and-white
`concept is generalized to a matter of degree. By doing this, one accomplishes two things:
`(1) ease of describing human knowledge involving vague concepts, and (2) enhanced abil-
`ity to develop a cost—effective solution to real—world problems.
`The term fuzzy logic in this book is most frequently used in the broad sense. When-
`ever it is used in the narrow sense, we will explicitly state so.
`
`The History of Fuzzy yogic
`1.2
`
`1.2.1 The Birth of Fuzzy Set Theory
`
`The idea of fuzzy sets was born in July 1964. Lofti A. Zadeh is a well-respected professor
`in the department of electrical engineering and computer science at University of Califor-
`nia, Berkeley. In the fifties, Professor Zadeh believed that all real—world problems could be
`solved with efficient, analytical methods and/0r fast (and big) electronic computers. In this
`direction, he has made significant contributions in the development of system theory (e.g.,
`the state variable approach to the solution of simultaneous differential equations) and
`computer science. In early 19603, however, he began to feel that traditional system analy-
`sis techniques were too precise for many complex real—world problems. In a paper written
`in 1961, he mentioned that a different kind of mathematics was needed:
`
`We need a radically diflerent kind ofmathematics, the mathematics offuzzy 0r
`
`cloudy quantities which are not described in terms of probability distribu-
`tions. Indeed, the needfor such mathematics is becoming increasingly appar-
`ent..., for in most practical cases the a priori data as well as the criteria by
`which the performance of a man-made system is judged are far from being
`
`Page 00005
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`

`

`—————__________________
`Section 1.2
`The History of Fuzzy Logic
`5
`
`
`
`In July 1964, Zadeh was in New York City visiting his parents and had plans to
`leave soon for Southern California, where he had been invited by Richard Bellman to
`spend part of the summer at Rand Corp. to work on problems in pattern classification
`and system analysis. With this upcoming work on his mind, his thoughts often turned to
`the use of imprecise categories for classification. One night in New York, Zadeh had a
`dinner engagement with some friends. It was canceled, and he spent the evening by him—
`self in his parents’ apartment. The idea of grade of membership, which is the concept
`that became the backbone of fuzzy set theory, occurred to him then. This important
`event led to the publication of his seminal paper on fuzzy sets in 1965 and the birth of
`fuzzy logic technology.
`The concept of fuzzy sets encountered sharp criticism from the academic commu-
`nity. Some rejected it because Of the name, without knowing the content in detail. Others
`rejected it because of the theory’s emphasis on imprecision —— a major departure from the
`Western scientific discipline’s focus on precision. In the late 1960s, it even was suggested
`to Congress as an example of the waste of government funds (much of Zadeh’s research
`was being funded by the National Science Foundation). A flurry of correspondence from
`Zadeh and emerged in defense of the work. However, the controversy concerning the
`fuzzy logic remains.
`
`1.2.2
`
`A Decade of Theory Development (1965 — 1975)
`
`Even though there was strong resistance to fuzzy logic, many researchers around the world
`became Zadeh’s followers. While Zadeh continued to broaden the‘foundation of fuzzy set
`theory, scholars and scientists in a wide variety of fields — ranging from psychology,
`sociology, philosophy, and economics to natural sciences and engineering—were explor-
`ing this new paradigm during the first decade after the birth of fuzzy set theory. Important
`concepts introduced by Zadeh during this period include fuzzy multistage decision-mak-
`ing, fuzzy similarity relations, fuzzy restrictions, and linguistic hedges. Other contribu—
`tions include R.E. Bellman’s work (with Zadeh) on fuzzy multistage decision making
`[33], G. Lakoff’s work from a linguistic View [346], J. A. Goguen’s work on the category-
`theoretic approach to fuzzify mathematical structure [213,212], L. J. Kohout and B. R.
`Gains on the foundation of fuzzy logic [200, 325], the work on fuzzy measures by R. E.
`Smith and M. Sugeno [543, 455, 557, 558], G. J. Klir, Sols and Meseguer’s work on fuzz-
`ified algebraic and topological systems [545 , 411], C. L. Chang’s work on fuzzy topology
`[108], Dunn and J. C. Bezdek’s work on fuzzy clustering [181], C. V. Negoita’s work on
`fuzzy information retrieval [443-445], the work by M. Mizumoto and K. Tanaka on fuzzy
`automata and fuzzy grammars [421—424], A. Kandel’s work on the fuzzy switching func—
`tion [294-295], and H. J. Zimmermann’s work on fuzzy optimization [718].
`During the first decade, many mathematical structures were firzzified by generalizing
`the underlying sets to be fuzzy. These structures include logics, relations, functions,
`graphs, groups, automata, grammars, languages, algorithms, and programs. One of the two
`early fuzzy logic journals in the world is actually a Chinese journal on fuzzy mathematics.
`It is rather unfortunate that fuzzy logic research in China, like all other academic research,
`
`Page 00006
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`

`

`# 0
`
`Introduction
`
`Chapter
`
`1
`
`In the late 1970s, a few small university research groups on fuzzy logic were estab-
`lished in Japan. Professor T. Terano and Professor H. Shibata from Tokyo University led
`one such group in Tokyo. A second research group in the Kanasai area was led by Profes—
`sor K. Tanaka from Osaka University and Professor K. Asai from the University of Osaka
`Prefecture. These researchers encountered an “anti-fuzzy” atmosphere in Japan during
`those early days. However, their persistence and hard work would prove to be worthwhile
`a decade later. These Japanese researchers, their students, and the students of their stu—
`dents would make many important contributions to the theory as well as to the applica—
`tions of fuzzy logic.
`An important milestone in the history of fuzzy logic control was established by
`Assilian and E. Mamdani in the United Kingdom in 1974. They developed the first fuzzy
`logic controller, which was for controlling a steam generator. They were initially compar-
`ing learning algorithms for adaptive control of a nonlinear, multidimensional plant for a
`physical steam engine but found that many learning schemes failed to even begin to con—
`verge on a reasonable time scale (running out of steam!). A fuzzy linguistic method was
`developed to prime the learning controller with an initial policy to speed the adaptation—
`the verbal statements of engineers were transcribed as fuzzy rules and used under fuzzy
`logic to form a control policy. The performance of these fuzzy linguistic controllers was so
`good in their own right, however, that they became central to a range of studies that subse-
`quently took place. As early as 1975, E. Mamdani and Baaklini already showed that fuzzy
`control rules may be tuned automatically by fuzzy linguistic adaptive strategies. Auto-
`matic learning and tuning of fuzzy rules would prove to be a very important area in the
`next two decades.
`
`Pioneering efforts to use fuzzy logic applications in civil engineering were made by
`C. B. Brown, D. Blockley, and D. Dubois. In April 1971, C. Brown and R. Leonard [90]
`introduced and discussed civil engineering applications of fuzzy sets during the ASCE
`Structural Engineering Meeting in Baltimore, Maryland. In 1975, D. Blockley [60] pub-
`lished a paper on the likelihood of structural accidents, which was followed by a continous
`flow of stimulating papers [59, 58] and a thought-provoking book [57]. In 1979, C. Brown
`[87] presented a fuzzy safety measure, with which more realistic failure rates were
`obtained by utilizing both subjective information and objective calculations. Later, Brown
`treated entropy constructed probabilities [88].
`In 1977, Dubois applied fuzzy sets in a comprehensive study of traffic conditions
`[163, 178]. The general problem of uncertainty and fuzziness in engineering decisionmak—
`ing was discussed in a comprehensive manner by J. Munro [431]. J. Yao summarized the
`development of civil engineering applications of fuzzy sets during the seventies in a 1985
`NSF workshop on civil engineering applications of fuzzy sets held at Purdue University in
`memory of Professor King-Sun Fu, who died in April 1985.
`One way to get an overall picture of the growth of fuzzy logic during the first
`decade is to study the number of papers published on the subject. Based on a survey
`conducted by B. Gaines, the number of papers increased by about 40 percent annually
`during the mid 1970s. Works accomplished during this period established the founda-
`tion of fuzzy logic technology and led to the development of application of this technol-
`
`Page 00007
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`

`

`a s
`
`7
`
`ection 1.2
`
`The History of Fuzzy Logic
`
`1.2.3
`
`Pioneers of Industrial Applications (1976 - 1987)
`
`In 1976, the first industrial application of fuzzy logic was developed by Blue Circle
`Cement and SIRA in Denmark. The system is a cement kiln controller that incorporates
`the “know-how” of experienced operators to enhance the efficiency of a clinker through
`smoother grinding. The system went to operation in 1982.
`After eight years of persistent research, development, and deployment efforts, Seiji
`Yasunobu and his colleagues at Hitachi put a fuzzy logic-based automatic train opera—
`tion control system into operation in Sendai city’s subway system in 1987. Another
`early successful induStrial application of fuzzy logic is a water-treatment system devel-
`oped by Fuji Electric. We should make a few important points about these applications.
`First, after a successful demonstration of these approaches, it took years for both
`projects to be deployed in real—world operation due to various concerns about this new
`technology from government officials. The roads traveled by these engineers were not
`easy at all. Second, these two applications became the major “success stories” of fuzzy
`logic technology in Japan. Consequently, many more Japanese engineers and companies
`started to investigate fuzzy logic applications. Third, both applications made significant
`contributions to the technology of fuzzy logic. The development of the Sundai subway
`system introduced an interesting architecture for using fuzzy logic for predictive con-
`trol. It also used fuzzy logic together with mathematical modeling, the former for rec—
`ommendng control options and for evaluating control options, and the latter for
`simulating control options to predict their effects. The development of water treatment
`systems enabled Fuji Electric to introduce the first Japanese general-purpose fuzzy logic
`controller (named FRUITAX) into the market in 1985.
`
`1.2.4
`
`The Fuzzy Boom (1987 - present)
`
`The fuzzy boom in Japan was a result of the close collaboration and technology transfer
`between universities and industries. In 1988, the Japanese goVemment launched a careful
`feasibility study about establishing national research projects on fuzzy logic involving
`both universities and industry. Two large-scale national research projects were established
`by two agencies — the Ministry of International Trade and Industry (MITI) and the Sci-
`ence and Technology Agency (STA). The project established by MITI was a consortium
`called the Laboratory for International Fuzzy Engineering Research (LIFE), which
`involved 50 companies with a six—year total budget of $5,000,000,’000.
`Matsushita Electric Industrial Co. (also known as Panasonic outside Japan) was the
`first to apply fuzzy logic to a consumer product, a shower head that controlled water tem-
`perature, in 1987. In late January 1990, Matsushita Electric Industrial Co. named their
`newly developed fuzzy controlled automatic washing macln'ne “Asai—go (beloved wife)
`Day Fuzzy” and launched a major commercial campaign for the “fuzzy” product. This
`campaign turned out to be a successful marketing effort not only for the product, but also
`for the fuzzy logic technology. A foreign word pronounced “fuzzy” was thus introduced to
`Japan with a new meaning — intelligence. Many other'home electronic companies fol—
`lowed Panasonic’s approach and introduced fuzzy vacuum cleaners, fuzzy rice cookers,
`
`Page 00008
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`

`

`fl
`
`
`
`Chapter
`
`1
`
`Introduction
`
`sumers (including children) in Japan all recognized the Japanese word “fuzzy,” which won
`the gold prize for a new word in 1990.
`This fuzzy boom in Japan triggered a broad and serious interest in this technology in
`Europe, and, to a lesser extent, in the United States, where fuzzy logic was invented. Sev-
`eral major European companies formed fuzzy logic task forces within their corporate
`Research and Development (R&D) divisions. They include SGS—Thomson of Italy, Sie-
`mens, Daimler-Benz, and Klockner—Moeller in Germany. In the United States, the General
`Electric Corporate Research Division and Rockwell International Science Center have
`both developed advanced fuzzy logic technology as well as their industrial applications.
`Fuzzy logic has found applications in other areas. The first financial trading system
`using fuzzy logic was Yamaichi Fuzzy Fund. It handles 65 industries and a majority of the
`stocks listed on Nikkei Dow and consists of approximately 800 fuzzy rules. Rules are
`determined monthly by a group of experts and modified by senior business analysts as
`necessary. The system was tested for two years, and its performance in terms of the return
`and growth exceeds the Nikkei Average by over 20 percent. While in testing, the system
`recommended “sell” 18 days before the Black Monday in 1987. The system went into
`commercial operation in 1988.
`
`1.2.5
`
`Tools for Implementing Fuzzy Logic Applications (1986 - present)
`
`Another important milestone in the history of fuzzy logic is the first VLSI chip for perforrn—
`ing fuzzy logic inferences developed by M. Togai and H. Watanabe in 1986 [590]. These
`special—purpose VLSI chips can enhance the performance of fuzzy rule-based systems for
`real-time applications. Togai later formed a company (Togai Infralogic) that sold hardware
`and software packages for developing fuzzy logic applications. Several other companies
`(e.g., APTRONIX, INFORM) were formed in the late 1980s and early 1990s. Even though
`these companies had some initial success, several did not survive through the mid— 1990s.
`This is partially due to the fact that vendors of conventional control design software such as
`MathWorks started introducing add—on toolboxes for designing fuzzy systems. The Fuzzy
`Logic Toolbox for MATLAB was introduced as an add—on component to MATLAB in 1994.
`
`1.2.6
`
`Fuzzy Logic in Education (1980 - present)
`
`The important issue about introducing fuzzy sets to undergraduate engineering and sci-
`ence curricula was discussed during a panel discussion of the first conference of NAFIPS
`(North American Fuzzy Information Processing Society) [660]. Participants include C. B.
`Brown, K. S. Fu, L. A. Zadeh, R. L. Yager, P. Smets, J. Bezdek, and T. Whalen. Colin
`Brown concluded the panel discussion with the following summary remarks:
`
`Engineering consists largely of recommending decisions based on insufiicient
`information and even ignorance on the basis of subjective acceptance crite-
`ria. It is essential that these students be exposed to ways of treating uncer-
`tainty and vagueness. This also requires that existing faculty utilize these
`methods. The problem is not just the provision of material on fuzzy sets and
`
`probability; the material has to be developed in professional courses.
`
`Page 00009
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`

`

`__————
`
`section 1.2
`
`The History of Fuzzy Logic
`
`9
`
`Indeed, the need to develop courses and textbooks for undergraduates and graduates,
`
`as well as training courses for practitioners in the industry has been voiced many times
`
`during conferences and workshops since then. We hope this book responds to such a need.
`
`1.2.7
`
`Toward A More Principled Design (1984 - present)
`
`The development of fuzzy systems in the early days required the manual tuning of the sys—
`tem parameters based on observing system performance. This drawback has become one
`of the major criticisms of fuzzy logic. Even though Mamdani and Baaklini introduced
`self-adaptive fuzzy logic control as early as 1975, the most common citation of the first
`work in this area is a paper by T. J. Procyk and E. H. Mamdani published in 1979. This
`was followed by Japanese researchers in the 19803. T. Takagi and his advisor M. Sugeno
`together took an important step by developing the first approach for constructing (not tun—
`ing) fuzzy rules using training data. Their approach developed fuzzy rules for controlling a
`toy vehicle by observing how a human operator controlled the vehicle. Even though this
`\important work did not gain as much immediate attention as it did later, it laid the founda—
`tion for a popular subarea in fuzzy logic, which is now referred to as fuzzy model identifi-
`cation in the 19903.
`
`Another trend that contributed to research in fuzzy model identification is the
`increasing Visibility of ‘neural network research in the late 19803. Because of certain
`similarities between neural networks and fuzzy logic, researchers began to investigate
`ways to combine the two technologies. The most important outcome of this trend is the
`developmentof various techniques for identifying the parameters in a fuzzy system
`using neural network learning techniques. A system built this way is called a neuro-
`fuzzy system. Bart Kosko has been known for his contribution to neuro-fuzzy systems.
`His books on neural networks and fuzzy logic (his was the first book on this topic) also
`introduced fuzzy logic to many readers who were not aware of the existence of the tech-
`
`nology previously [332].
`The 1990s is an era of new computational paradigms. In addition to fuzzy logic
`and neural networks, a third nonconventional computational paradigm has also become
`popular—evolutionary computing, which includes genetic algorithms, evolutionary
`strategies, and evolutionary programming. Genetic Algorithms(GAs) and evolutionary
`strategies are optimization techniques that attempt to avoid being easily trapped in local
`minima by simultaneously exploring multiple points in the search space and by generat—
`ing new points based on the Darwinian theory of evolution—survival of the fittest. The
`popularity of GA in the 19903 inspired the use of GA for optimizing parameters in
`fuzzy systems.
`The various combinations of neural networks, genetic algorithms, and fuzzy logic
`help people to View them as complementary. To distinguish them from the conventional
`methodologies based on precise formulations, Zadeh introduced the term soft computing
`in the early 19903.
`The history of fuzzy logic research and application development continues as you
`read this book. We hope that you can contribute to this history in the near future as well.
`
`Page 00010
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`

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`
`
`
`
`
` 1Chapter Introduction
`
`1.3 Motivations
`
`Fuzzy logic was motivated by two objectives. First, it aims to alleviate difficulties in
`developing and analyzing complex systems encountered by conventional mathematical
`tools. Second, it is motivated by observing that human reasoning can utilize concepts
`and knowledge that do not have well—defined, sharp boundaries (i.e., vague concepts).
`The first motivation is directly related to solving real-world problems, while the second
`motivation is related to artificial
`intelligence—the discipline in computer science
`involved with developing computer systems that exhibit intelligent behaviors similar to
`those of human beings. The former motivation requires fuzzy logic to work in quantita-
`tive and numeric domains, while the latter motivation enables fuzzy logic to have a
`descriptive and qualitative form because vague concepts are often described qualita-
`tively by words. These two motivations together not only make fuzzy logic unique and
`different from other technologies that focus on only one of these goals but also enable
`fuzzy logic to be a natural bridge between the quantitative world and the qualitative
`world. As will become clear at a later point, this unique characteristic of fuzzy logic
`allows this technology to offer an important benefit—it not only provides a cost-effec—
`tive way to model complex systems involving numeric variables but also offers a quali-
`tative description of the system that is easy to comprehend.
`
`1.3.1
`
`The Underpinning: The Principle of Incompatibility
`
`The underpinning of a fuzzy logic approach to achieve the two objectives described above
`is based on an observation about a fundamental trade-off between precision and cost ——
`which is referred to by L. A. Zadeh as the principle of incompatibility. In one of his semi—
`nal papers, Zadeh eXplained this observation:
`
`Stated informally, the essence of this principle is that as the complexity of a
`system increases, our ability to make precise yet significant descriptions
`about its behavior diminishes until a threshold is reached beyond which
`precision and significance (or relevance) become almost mutually exclu-
`sive characteristics.
`
`In other words, one has to pay a cost for high precision. Therefore, the cost for pre-
`cise modeling and analysis of a complex system can be too high to be practical. An exam-
`ple often used by Zadeh to illustrate this trade-off is the problem of parking a car. Usually,
`it takes a driver less than half a minute to parallel park. However, if we were asked to park
`a car in a parking space sUch that the outside wheels are precisely within 0.01 mm from
`the side lines of a parking space, and the wheels are within 0.01 degree from a specified
`angle, how long do you think it would take you to park the car? It would take me a very
`long time. In fact, I would probably give up after trying ten minutes or so. The point is that
`the cost (i.e., the time required) to park a car increases as the precision of the car parking
`task increases. This trade—off between precision and cost exists not only in car parking but
`also in’ control, modeling, decision making, and almost any kind of problem.
`Conceptually, we can use Fig 1.2 to depict this trade-off for many systems. The hori—
`
`Page 00011
`
`

`

`
`
`Section 1.3
`
`Motivations
`
`11
`
`pose of representing both the cost and the degree of utility. As the precision of a system
`increases, the cost for developing the system also increases, typically in an exponential
`manner. On the other hand, the utility (i.e., usefulness) of the system does not increase
`proportionally as its precision increases — it usually saturates after a certain point. This
`insight about the trade—off between precision, cost, and utility inspired Zadeh and his fol-
`lowers to exploit the gray area in Fig 1.2, which resulted in a revolutionary way of think-
`ing for developing approximate solutions that are both cost-effective and highly useful. In
`other words, the fundamental principle of fuzzy logic is to develop cost-effective approxi-
`mate solutions to complex problems by exploiting the tolerance for imprecision.
`Traditionally, fuzzy logic has been Viewed as a theory for dealing with uncertainty
`about complex systems. From the discussion above, however, it seems even more suitable
`to view fuzzy logic as an approach for approximation theories. This perspective on fuzzy
`logic brings to the surface one of its ultimate concerns — low cost. Indeed, providing a
`low cost solution to a wide range of real—world problems is the primary reason that fuzzy
`logic has found so many successful applications in industry to date. Understanding this
`driving force of the success of fuzzy logic will prevent us from falling into the trap of
`debating with critics “whether fuzzy logic can accomplish what X cannot accomplish”
`where X is an alternative technology such as probability theory, control theory, etc. Such a
`debate is usually not fruitful because it ignores one important issue— cost. A better ques—
`tion to ask is, “What is the difference between the cost of a fuzzy logic approach and the
`cost of an approach based on X to accomplish a certain task?” In a panel discussion on
`fuzzy logic and neural networks held at the NASA Johnson Space Center in 1991, K.
`I-Iirota, an internationally known fuzzy logic researcher from Japan, made a short, yet
`sharp, comment by saying, “There is a fundamental difference between the theoretically
`possible and the practically feasible.” People with this insight can more easily recognize
`and appreciate the benefits offered by fuzzy logic.
`
`FIGURE 1.2
`
`The Cost-Precision Trade-off
`
`A
`
`Cost
`
`
`
`Utility
`
`’-
`
`Page 00012
`
`

`

`E 1
`
`Introduction
`1
`Chapter
`
`
`
`1.3.2
`
`A Quest for Precision Forever?
`
`Even though the precision—cost trade-off principle is intuitive, the idea of not pursuing pre—
`cision all the time is actually not easy. Precision has often been viewed as “desirable,”
`while imprecision has been considered “undesirable.” This is especially true in the field of
`science and engineering. It is true that precise problem formulation enables scientists and
`engineers to use a Wide range of mathematical tools to develop and analyze solutions in a
`rigorous way. It is also true that this quest for precision has contributed to the rapid devel-
`opment of basic science and applied technology in the twentieth. century. However, as
`technology advances, so does the complexity of the problems facing us. While the quest
`for precision will continue and will remain beneficial to human society to a certain extent,
`fuzzy logic brings a complementary viewpoint into the world — a View in which cost—
`effectiveness rather than precision is the ultimate concern.
`
`1.4
`Why Use Fuzzy Logic for ContrOl?
`
`
`One common answer to this question is that fuzzy logic can be used for controlling a pro—
`cess (i.e., a plant in control engineering terminology) that is too nonlinear or too ill-under-
`stood to use conventional control designs. Another answer is that fuzzy logic enables
`control engineers to easily implement control strategies used by human operators. The first
`answer echoes the first motivation for fuzzy logic — to deal with complex systems —
`while the second answer is related to the second motivation — the ease of describing
`human knowledge. We will illustrate these points using a real-world application below.
`Before we do that, though, we would like to point out that fuzzy logic control broadens the
`range of applications of control engineering tools and methods. It is not meant to replace
`but rather to augment existing methodologies for control design. We will return to this
`important point in a later chapter.
`
`1.4.1
`
`Modus Operandi of Fuzzy Logic
`
`The distinguishing mark of fuzzy logic in rule-based systems is its ability to deal with
`situations in which making a sharp distinction between the boundaries of application in
`the use of rules or constraints is very difficult. An example that clearly illustrates this
`fact is one that is taken from an actual application of fuzzy logic control and one of its
`seminal ones, namely fuzzy logic-based image stabilization in camcorders. Here there
`are no known algorithms that would in a structured manner determine the compensation
`strategy. For this reason, one would rely on rules or heuristics as the basis for implemen-
`tation of a control strategy. In particular, in order to determine whether the present
`image is a function of the movement of the camera or of the movement of objects1n the
`field of view, the designers1 have chosen to mark certain objectsin the field of View as
`references. Further, the position of reference objects1n two subsequent frames13 related
`
`
`
`Page 00013
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`_
`
`Section 1.4 Why Use Fuzzy Logic for Control?
`
`13
`
`in terms of four motion vectors, one for each subarea in the image. An example of
`
`heurstic rules is given below:
`If all motion vectors are almost parallel and their time difierential is small, then the
`hand jittering is detected and the direction of the hand movement is the direction of the
`
`moving vectors.
`Heuristic rules of this kind are used to deduce whether the differences in two consecu-
`
`tive frames are due primarily to the motion of the camera, or represent true motion of
`objects in the field of View. Thus as shown in Fig 1.3, the image on the left would be
`interpreted as being based on the motion of the camera since all motion vectors are in
`the same direction, while the image on the right is interpreted as bein