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Fuzzy thinking: The new Science of fuzzy logic
384
Bulletin
also for researchers engaged in this fieJJ because of its abw,dant contents. Wang Pei-hua
Changsha Normal University of Water Resources and Electric Power ZIP.410077, Hunan, China Fuzzy Thinking: The N e w Science o f Fuzzy Logic At l a s t - a popular exposition of fuzzy logic. Fuzzy technology is at the heart of several expert systems and process controllers, including several Japanese consumer products such as energy optimizing washing machines and shake-free video cameras. Fuzzy passenger train controllers save electricity and give a smoother ride. Other applications include lift and cement kiln controllers and financial trading rooms. These are listed in the book by Bart Kosko (Hyperion, New York, 1992, ISBN 1-58282-839-8. A few advanced systems can learn t o o - u s i n g neural network techniques that generate fuzzy rules. Kosko's version of these adaptive fuzzy systems is based on the observation that crisp sets correspond to the corners of a hypercube, which are the attractors of Anderson's 'brain state in a box' model of neural nets. The internal points of the cube correspond to fuzzy subsets. This book makes the mathematics very accessibl~ to the lay reader in a style similar to James Gieick's journalistic book on Chaos or Hawking's informed but rather smug Brief History of Time. As a book on popular science it is, in my humble opinion, ten times better than Hawking through not quite up to the standard of my favourites: Capra's The Tao of Physics, Eistein's exposition of special re:ativity and Layzer's Cosmogenesis. Nevertheless it stands comparison with these, especially those parts that explain Kosko's own contribution on fuzzy neutral networks, despite a few eccentricities. In the expert systems field the comparable popular book that springs to mind most is Feigenbaum and McCorduck's Fifth Generation, which shared Kosko's rather gung-ho view of the possibilities of technology. Kosko makes great play of the success of fuzzy set theory in the East and the hostility with which it has been received in the West. He attributes "his to a pervasive Eestern Buddhist tradition wher,=~in ~ri3totle's law, of the excluded middle, which says that both A and not-A can never be true, never counted for much. There is a slight error in the chronology where Kosko argues that Buddha influenced Lao-tzu who, as I recall it, lived at about the same time. It is not clear that Lao-tzu was an historical person and the name means 'old teacher'. Just as the Dead Sea scrolls indicate for Jesus of Nazareth, it appears that Lao-tzu may be a composite of several historical actors. Kosko also omits to mention a significant stream of Western anti-Aristotelianism stretching through Hegel to Trotsky and possibly as far back as Spinoza and based on the pre-Socratic Greeks such as Heraclitus. These thinkers rejected several of Aristotle's tenets (notably that n o t - n o t - A = A) and not just the excluded middle. So when Kosko quotes Mao's
interesting essay On Contradiction he fails to observe that Mao had a foot in both camps, even if his view of the Hegelian and Marxist traditions had been clouded by Stalin's vulgar influence. Despite this, I was pleased to see that this is the only book on expert systems other than mine [1] to use the symbol of the supreme ultimate (or tai chi) ~) to make the connexion oetween fuzziness and the interpenetration of opposites. I took issue with one technical point. It is claimed that the additive fuzzy logic used in process control provides a good model of legal and other kinds of decision making. As Peter Jones and I pointed out in 1988 [1] this is not so, because the moments defuzzification method pro;ides continuous output for continuous input, whereas decisions represent discontinuous output states usually. The mean-of-maxima method of defuzzifying is nearly always preferable. Apart from the clear introduction to the most exciting parts of fuzzy logic, the finest parts of this generally well written book are the cameo portraits of several of the personalities of the fuzzy sets community (Zadeh, Sugeno, Yamakawa, etc.) and the portrayal of the venom directed at them over the years by the mainstream scientific and artificial intelligence communities. The major weakness is a tendency to argue that fuzzy thinking can explain and resolve every issue from abortion to the existence of God, but it's great fun; anti-abortion cranks and euthanasiasts will have to .~ubmit to the fuzzy curves of public opinion. Nothing is left unscathed; ethics, law, drugs, p o l i t i c s - a l l human life can be scrutinized through the microscope of fuzzy logic. When Kosko delves into using fuzzy logic to model legal decisions it becomes clear that he has not, after all, broken completely with the Western, pragmatist tradition in which he was educated, for he makes the mistake of many other critics and supporters of AI in assuming that knowledge or intelligence exists in the heads of individuals rather than in the social nexus that they inhabit as well. Another apparent non sequitur is his 'proof' that the universe is not nothing. Here makes twe errors; first in arguing by r e d u c t i o - w h i c h would make his proof ,macceptable to many m a t h e m a t i c i a n s - b u t more seriously by taking the complement of the universe (I) without saying in what 'universe' he is taking the complement. But these are minor niggles compared to the generally beneficial reading experience the book suppl!es. If you have heard of fuzzy logic and want to know what it is all about then buy this book. It is not only a good popularization, it's the only one you are likely to see for quite ~ while. I think Kosko has done the world a service and will undoubtedly be inflicting this book as a gift on all those people who have asked me 'Well, what exactly is all this fuzzy stuff?; when I'm far to tired or inebriated to reply sensibly. Recommendedl
Reference (1) I.M. Graham and P.L.K. Jones, ExpertSystems: Knowledge, Uncertaintyand Decision(Chapman & Hall, London, 1988). lan Graham
Bulletin
also for researchers engaged in this fieJJ because of its abw,dant contents. Wang Pei-hua
Changsha Normal University of Water Resources and Electric Power ZIP.410077, Hunan, China Fuzzy Thinking: The N e w Science o f Fuzzy Logic At l a s t - a popular exposition of fuzzy logic. Fuzzy technology is at the heart of several expert systems and process controllers, including several Japanese consumer products such as energy optimizing washing machines and shake-free video cameras. Fuzzy passenger train controllers save electricity and give a smoother ride. Other applications include lift and cement kiln controllers and financial trading rooms. These are listed in the book by Bart Kosko (Hyperion, New York, 1992, ISBN 1-58282-839-8. A few advanced systems can learn t o o - u s i n g neural network techniques that generate fuzzy rules. Kosko's version of these adaptive fuzzy systems is based on the observation that crisp sets correspond to the corners of a hypercube, which are the attractors of Anderson's 'brain state in a box' model of neural nets. The internal points of the cube correspond to fuzzy subsets. This book makes the mathematics very accessibl~ to the lay reader in a style similar to James Gieick's journalistic book on Chaos or Hawking's informed but rather smug Brief History of Time. As a book on popular science it is, in my humble opinion, ten times better than Hawking through not quite up to the standard of my favourites: Capra's The Tao of Physics, Eistein's exposition of special re:ativity and Layzer's Cosmogenesis. Nevertheless it stands comparison with these, especially those parts that explain Kosko's own contribution on fuzzy neutral networks, despite a few eccentricities. In the expert systems field the comparable popular book that springs to mind most is Feigenbaum and McCorduck's Fifth Generation, which shared Kosko's rather gung-ho view of the possibilities of technology. Kosko makes great play of the success of fuzzy set theory in the East and the hostility with which it has been received in the West. He attributes "his to a pervasive Eestern Buddhist tradition wher,=~in ~ri3totle's law, of the excluded middle, which says that both A and not-A can never be true, never counted for much. There is a slight error in the chronology where Kosko argues that Buddha influenced Lao-tzu who, as I recall it, lived at about the same time. It is not clear that Lao-tzu was an historical person and the name means 'old teacher'. Just as the Dead Sea scrolls indicate for Jesus of Nazareth, it appears that Lao-tzu may be a composite of several historical actors. Kosko also omits to mention a significant stream of Western anti-Aristotelianism stretching through Hegel to Trotsky and possibly as far back as Spinoza and based on the pre-Socratic Greeks such as Heraclitus. These thinkers rejected several of Aristotle's tenets (notably that n o t - n o t - A = A) and not just the excluded middle. So when Kosko quotes Mao's
interesting essay On Contradiction he fails to observe that Mao had a foot in both camps, even if his view of the Hegelian and Marxist traditions had been clouded by Stalin's vulgar influence. Despite this, I was pleased to see that this is the only book on expert systems other than mine [1] to use the symbol of the supreme ultimate (or tai chi) ~) to make the connexion oetween fuzziness and the interpenetration of opposites. I took issue with one technical point. It is claimed that the additive fuzzy logic used in process control provides a good model of legal and other kinds of decision making. As Peter Jones and I pointed out in 1988 [1] this is not so, because the moments defuzzification method pro;ides continuous output for continuous input, whereas decisions represent discontinuous output states usually. The mean-of-maxima method of defuzzifying is nearly always preferable. Apart from the clear introduction to the most exciting parts of fuzzy logic, the finest parts of this generally well written book are the cameo portraits of several of the personalities of the fuzzy sets community (Zadeh, Sugeno, Yamakawa, etc.) and the portrayal of the venom directed at them over the years by the mainstream scientific and artificial intelligence communities. The major weakness is a tendency to argue that fuzzy thinking can explain and resolve every issue from abortion to the existence of God, but it's great fun; anti-abortion cranks and euthanasiasts will have to .~ubmit to the fuzzy curves of public opinion. Nothing is left unscathed; ethics, law, drugs, p o l i t i c s - a l l human life can be scrutinized through the microscope of fuzzy logic. When Kosko delves into using fuzzy logic to model legal decisions it becomes clear that he has not, after all, broken completely with the Western, pragmatist tradition in which he was educated, for he makes the mistake of many other critics and supporters of AI in assuming that knowledge or intelligence exists in the heads of individuals rather than in the social nexus that they inhabit as well. Another apparent non sequitur is his 'proof' that the universe is not nothing. Here makes twe errors; first in arguing by r e d u c t i o - w h i c h would make his proof ,macceptable to many m a t h e m a t i c i a n s - b u t more seriously by taking the complement of the universe (I) without saying in what 'universe' he is taking the complement. But these are minor niggles compared to the generally beneficial reading experience the book suppl!es. If you have heard of fuzzy logic and want to know what it is all about then buy this book. It is not only a good popularization, it's the only one you are likely to see for quite ~ while. I think Kosko has done the world a service and will undoubtedly be inflicting this book as a gift on all those people who have asked me 'Well, what exactly is all this fuzzy stuff?; when I'm far to tired or inebriated to reply sensibly. Recommendedl
Reference (1) I.M. Graham and P.L.K. Jones, ExpertSystems: Knowledge, Uncertaintyand Decision(Chapman & Hall, London, 1988). lan Graham