Never heard of fuzzy logic? Possible. Never used fuzzy logic? Unlikely. Since 1965, when University of California at Berkeley mathematician Lotfi A. Zadeh laid the ground for this approach in a paper entitled "Fuzzy Sets," his ideas have intrigued engineers. Fuzzy technology is now used in many devices we use in our daily lives - ranging from video cameras to washing machines to cars and even automatically operated underground trains. Fuzzy logic is used in process control, expert and decision support systems, data analysis, and process modeling.

At the core of fuzzy logic is the concept of fuzzy sets. To understand what is special about these sets, start with the definition of a conventional "crisp" set: a set to which any given element either distinctly does or distinctly does not belong. With fuzzy sets, membership is less strict: an element can be a member of a set to a certain degree, while at the same time belonging to other sets to different degrees. This way of classifying elements matches our normal perceptions much more closely than do conventional crisp classifications.

For instance, when we talk about tall people, fast cars, or short vacations, we have a hard time drawing the line - is someone tall at 190 cm? Certainly. How about 180 cm? Probably. 179 cm? 178 cm? When exactly is someone no longer tall, but medium sized? When is a car fast, when is a vacation short? Fuzzy sets allow us to express mathematically the gradual continuum from tall to medium to short as humans perceive it, because elements can belong to more than one set. This is expressed through so-called membership functions that convert our vague notions of category membership into numerical values - usually normalized to the interval between 0 and 1, where 1 means that an element belongs completely to the set. Thus, we might say that a 190-cm person is tall to a membership degree of 1, a 178-cm person is tall to a degree of 0.7 and at the same time medium sized to a degree of 0.3, and a 168-cm person is tall to a degree of 0 and medium sized to a degree of 1.

Engineers are often faced with control problems that are easy to describe verbally, but tough to translate into the numerical terms required for automated process control. For example, the regulation of a hot-water heating system can be described as follows: "If it is cold outside, and the radiator is cool, pump a lot of hot water through the system; but if it is cold outside, and the radiator is warm or hot, pump a moderate amount of hot water; and if it is hot outside do not pump any hot water at all."

With fuzzy sets and algorithms that have been developed to express this sort of rule numerically, fuzzy control systems today operate successfully in many fields of engineering. Perhaps the first prominent example is the automatic train operator that has controlled the subway system of Sendai, Japan since 1986-1987. Back then it made headlines worldwide because it performed better than any human operator. Another widespread application is in video cameras, where fuzzy logic is used to compensate for vibration. These and numerous other examples demonstrate that the technology works - and, despite its name, can efficiently model and control high-precision processes.

Vague concepts abound in biology, medicine, and related fields, where biological variability is the order of the day. Surprisingly, however, fuzzy logic has received very little attention from biological scientists. Even in fields where modeling of highly complex systems is crucial, such as environmental science, elaborate arrays of differential equations are frequently applied, but little has been done to exploit the possibilities of fuzzy logic. This is particularly paradoxical given that, although deterministic and stochastic models can often be fitted to biological data sets, because the data are usually vague (or fuzzy) to begin with, it tends to be very difficult to validate such models.

Fuzzy techniques have many potential uses in the biological sciences - in essentially any area where it is necessary to analyze complex data, from ecotoxicology to medical imaging. Fuzzy expert systems are increasingly used in medicine to assist physicians in diagnosing cancer and other disorders. The journal Ecological Modelling has dedicated two special issues since 1996 to fuzzy logic, and there is even an informal organization of scientists called Artificial Intelligence Research in Environmental Science (AIRIES), whose members investigate possible environmental science applications of AI tools such as fuzzy logic and neural networks.

For my doctoral thesis, I investigated fuzzy controllers as a means of modeling pesticide volatilization and volatility, which are a potential major cause of pesticide contamination in nonagricultural areas. While this constituted only a very limited journey into the world of fuzzy logic, I was very happy with the results. I discovered that fuzzy controllers can be a very efficient means of communicating "expert knowledge" to others. In the course of my studies, I naturally read hundreds of papers dealing with pesticide volatilization, and from them as well as my own experiments I gained a great deal of insight into this complex process. I was then able to implement this knowledge in my fuzzy controllers - small, easy-to-use applications that allow my successors at the Institute of Ecological Chemistry of the German Federal Biological Research Centre for Agriculture and Forestry to reproduce my knowledge and understanding of volatilization without my having to be there.

While the term "fuzzy" may, as Zadeh suggests in a recent interview, have been an unfortunate choice - because it doesn't sound all that scientific - researchers should not be deterred by this. There is a lot of hard math behind fuzzy logic (although fortunately one doesn't need to study all of it in order to apply the logic) and, by now, plenty of evidence for its usefulness. So, any time you are facing a complex system and tough data analysis tasks, or would like to make your knowledge available to other people in an easily accessible way, you should consider fuzzy logic and its applications as a tool that could serve you well.

Ulrike Walter is a trained biologist and agricultural scientist who now works as a freelance English-to-German translator, specializing in the biosciences, medicine, and information technology.

Andrzej Krauze is an illustrator, poster maker, cartoonist, and painter who illustrates regularly for HMS Beagle, The Guardian, The Sunday Telegraph, Bookseller, and New Statesman.

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Endlinks

Building Fuzzy Expert Systems - an excellent online tutorial by William Siler. The site also provides text files ready for downloading and a demo version of the expert system shell used in the tutorial.

Fuzzy Logic and Neurofuzzy Resources - this list of links to research groups, software, hardware, commercial companies, conferences and workshops, tutorials, and much more in the field of fuzzy and systems and neural networks is maintained by the Image, Speech and Intelligent Systems (ISIS) research group at the University of Southampton.

Fuzzy Logic in Environmental Sciences - a list (including contact information) of people and organizations interested in applying fuzzy logic in various fields within the environmental sciences.

Fuzzy Shower Control - an online demonstration of fuzzy control using the control of water flow and temperature in a shower as an example.

Pesticide Volatilization: A Comparison of Methods for Measuring and Approaches to Fuzzy Logic Modeling - author's doctoral thesis, incorporating fuzzy logic, may be purchased from a German-language (and -currency) site.