Fuzzy Wuzzy was a bear,
Fuzzy Wuzzy had no hair.
So Fuzzy Wuzzy wasn't very fuzzy.
Was he?
It would be unfortunate if one only regarded fuzzy logic about as seriously as he or she regards the above children's poem. Though it sports an unconventional name, fuzzy logic is a field that has risen to the forefront of modern technology. Fuzzy technology was first developed in the United States, but it has truly bloomed into a billion dollar industry in Japan. The U.S., by some estimates, trails Japan by ten years in developing fuzzy logic applications.
Fuzzy logic is a mathematical approach to problem solving. It excels in producing exact results from imprecise data, and is especially useful in computers and electronic applications. Fuzzy logic differs from classical logic in that statements are no longer black or white, true or false, on or off. In traditional logic an object takes on a value of either zero or one; in fuzzy logic, a statement can assume any real value between 0 and 1, representing the degree to which an element belongs to a given set. The human brain can reason with uncertainties, vagueness, and judgments. Computers can only manipulate precise valuations. Fuzzy logic is an attempt to combine the two techniques.
In order to apply fuzzy logic to a particular system, a programmer must first make a "fuzzy model," a set that describes the system and how to handle it. Making such a model involves analyzing a problem and setting up the proper rules to define it, a process called fuzzification. After testing a given fuzzy model, a programmer evaluates the efficiency of the fuzzy rules and adjusts the model accordingly. For example, suppose you wanted to set up a fuzzy set to control the speed of an air conditioner's fan. An ordinary or computer-driven thermostat would require you to specify at exactly what temperature the fan should turn off. The thermostat would then measure the current temperature, and if it were above the specified temperature, it would turn on the fan at full blast until the desired temperature was reached. This is not very efficient, especially when compared with a fuzzy controller. Using a fuzzy logic controller, you could specify a range of temperatures that would be considered cold, cool, comfortable, warm, and hot. The fuzzy rules would control fan speed based on temperature range. For example, if your setting were on "comfortable", and the current temperature were "hot," then the fan would run at full blast; but if instead the temperature were "warm," the fan would run at a moderate speed. Once the desired temperature was reached, the fan would not just shut off and wait for the temperature to rise again; it would adjust its speed to maintain the desired temperature.
Fuzzy logic has certain advantages over traditional logical systems. Fuzzy logic systems are, for the most part, easy to set up and use. The results are accurate, and the technique need not be used alone; it can be employed in conjunction with other analytic methods. It is, however, best applied to relatively complex systems and systems with nonlinearities or uncertainties: traditional methods will probably work just as well when an environment is simple. The primary difficulty in using fuzzy logic is that the programmer must first thoroughly understand the intracacies of and be able to precisely define a problem, and then must be able to evaluate and fine-tune the results. Critics of fuzzy logic systems in fact contend that these systems, in part because they are not entirely analytic and thus involve fine-tuning, are unstable. Nonetheless, developments in neural networks may someday remedy this problem by enabling a computer to learn how to define the problem, set up rules, and perform any necessary fine-tuning itself.
Paul Wang, Ph.D., is a professor of electrical engineering at Duke and one of the world's foremost fuzzy logicians. He discussed in an interview with the authors the origins of the discipline of fuzzy logic and the implications of the rapid recognition which it has just recently gained.
The field was developed and the term "fuzzy logic" coined in the mid-1960's by Lotfi A. Zadeh, currently a professor at the University of California at Berkeley. When, in the 1970's, Dr. Wang first studied fuzzy logic, it was still considered an "underground" science; businesses and the government wouldn't sponsor research without evidence of practical usefulness. The first fuzzy logic class he taught at Duke had only three students, but meanwhile, through his own efforts, Dr. Wang became editor of the Information Science Journal, which was responsible for publishing many of the first articles in the field of fuzzy logic. One of Wang's graduate students, Masaki Togai, helped develop the first "fuzzy chip" and founded the first U.S. company devoted to the research and promotion of fuzzy technology. Togai Infralogic, based in California, is currently one of the world's largest vendors of fuzzy technology.
While recognition of the legitimacy of fuzzy logic has been a long time coming in the United States, it has finally come in force. Government institutions like the National Science Foundation have begun to sponsor research in the field. Products integrating fuzzy technology, such as camcorders and camera flashes, are being widely marketed. Articles about fuzzy technology appear in both scientific and general magazines. Bart Kosko has published a popular book about fuzzy logic, Fuzzy Thinking, that has already been translated into several languages. And, about ninety conferences on the field are held annually in the U.S., one of the largest of which is sponsored by Duke University and chaired by Dr. Wang.
During the Second International Conference on Fuzzy Theory & Technology, held October 13-16, 1993 at the Sheraton University Center in Durham, Lotfi A. Zadeh received the Premier Best Paper Award for his 1965 work "Fuzzy Sets". Although Zadeh has received numerous accolades abroad, this is one of his first awards in the States. The conference featured expert speakers from five continents and representatives from many businesses. Almost one hundred papers, with titles such as "A New Characterization of Fuzzy Logic Operators Producing Homomorphic-Like Conjunction-Disjunction Combinations between All Fuzzy Sets and Their One-Point Coverage-Equivalent Classes of Random Sets" and "Fuzzy Ideals & Fuzzy Bi-ideals in Fuzzy Semigroups," were presented and discussed in a span of four days.
Conferences such as this one are extremely important to the continuation of support for and research in fuzzy logic, for they serve to further interest in a field that will likely one day be an integral part of many future technological advances. Companies throughout the world, most notably in Japan, are already using fuzzy technology in consumer products. FIDE (Fuzzy Inference Development Environment,) FuziWare, and similar companies are marketing software with claims of improved productivity. Fuzzy logic has been implemented in computers, in the production of vehicles and home and business appliances, and in numerous other areas. The power of fuzzy technology has even been harnessed by the military. Yet, while the United States and several other countries are scrambling to produce new advances in this intriguing field, Japan is still a few years ahead of everyone else in the race to successfully apply fuzzy technology. It is unclear what role global techno-politics will play in the future of fuzzy logic, but it is certain that the repercussions will be felt far beyond the engineering laboratory. It is the hope of Paul Wang that Duke will continue to be at the crest of this technological wave.
The authors thank Dr. Paul Wang for his time and expertise.
Winter 1994 contents
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