"Fuzzy Logic is basically a multivalued logic that allows intermediate values to be defined between conventional evaluations like yes/no, true/false, black/white, etc. Notions like rather warm or pretty cold can be formulated mathematically and processed by computers." - Bauer et al.

FAQ: Fuzzy Logic and Fuzzy Expert Systems. From Mark Kantrowitz. Don't miss FAQ #2, What is Fuzzy Logic?

Fuzzy logic comes to life. By Nicholas Sheble. InTech (October 19, 2006). "The term 'fuzzy logic,' sounds nonsensical. 'That’s a problem,' declared R. Russell Rhinehart who heads the chemical engineering school at Oklahoma State University. He gave a couple of tutorials on artificial intelligence as part of a sponsored series of R&D updates Wednesday in the Standards Theater at ISA EXPO 2006 in the Reliant Center. 'The concepts of fuzzy logic are simple, but the jargon obscures that. In fact, fuzzy is absurdly simple.' It is Rhinehart’s contention the chemical industries under appreciate and under utilize fuzzy logic. Fuzzy logic applies like this. Say you have an apple. You take a bite out of the apple. Is it still an apple? You take another bite out of the apple. Now, is it still an apple? And another bite. And then, another bite. At some point, people will no longer perceive it as an apple. 'Fuzzy logic can represent this process,' Rhinehart explained. 'It becomes less of an apple as you move along. Fuzzy logic can assign percentages of belongingness to the process. It’s not a digital sort of situation where it’s either a one (1) or a zero (0). It’s either an apple, or it’s not.' ... Degrees of truth are often confused with probabilities. However, they are conceptually distinct; fuzzy truth represents membership in vaguely defined sets, not the likelihood of some event or condition. ... Fuzzy logic controls household appliances such as washing machines, which sense load size and detergent concentration and adjust their wash cycles accordingly, and refrigerators. ... 'You can use fuzzy to incorporate anticipatory behavior into a process, and it’s the type of prediction that is like the intuitive knowledge that a human operator of that process has,' concluded Rhinehart."

% of Michael Berthold's Fuzzy Logic Tutorial presented at ACAI-05 (Advanced Course on AI) and available from VideoLectures. "The tutorial will introduce the basics of fuzzy logic for data analysis. Fuzzy Logic can be used to model and deal with imprecise information, such as inexact measurements or available expert knowledge in the form of verbal descriptions. We will first introduce the concepts of fuzzy sets, degrees of membership and fuzzy set operators. After discussions on fuzzy numbers and arithmetic operations using them, the focus will shift to fuzzy rules and how such systems of rules can be derived from available data."

A Touch of Gray - Fuzzy logic has certain major advantages over traditional Boolean logic when it comes to microchip and applications design, yet its power is only just being harnessed by U.S. engineers and manufacturers. A talk with Paul Wang, Ph.D., Professor of Electrical Engineering, about this fascinating field. By Tung Tran and Ali Zomorodi. Vertices 10(1) Winter 1994. "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."

Fuzzy Logic Tutorial. By Steven D. Kaehler of the Seattle Robotics Society.

A Brief Course in Fuzzy Logic and Fuzzy Control. By Peter Bauer, Stephan Nouak, and Roman Winkler. Available from ESRU [Energy Systems Research Unit], Department of Mechanical Engineering. University of Strathclyde.

• Be sure to see their impressive collection of fuzzy logic applications.

What is 'fuzzy logic' ? Are there computers that are inherently fuzzy and do not apply the usual binary logic? From Scientific American's "Ask the Experts." Read the diverse responses from the experts and check out the collection of Related Links at the bottom of their page.

What is neuro-fuzzy logic? By Surjit Singh Bhatti. The Tribune (Chandigarh, India; October 24, 2002). "While fuzzy logic uses approximate human reasoning in knowledge-based systems, the neural networks aim at pattern recognition, optimisation and decision making. A combination of these two technological innovations delivers the best results. This has led to a new science called neuro-fuzzy logic in which the explicit knowledge representation of fuzzy logic is augmented by the learning power of simulated neural networks."

Fuzzy Logic. Quickstudy by Russell Kay. Computerworld (August 30, 2004). "The digital computing world is built on a structure of Boolean logic applied to binary values -- one or zero, yes or no, in or out. But this powerful structure is a gross oversimplification of the real world, where many shades of gray exist between black and white. In everyday life, we use quasimetric notions that are clearly related to numerical concepts or values but lack precision or demarcation. ... The real world simply doesn't map well to binary distinctions, and numerical precision is often unhelpful in making qualitative statements. Fuzzy logic gives us a way to deal with such situations. In fuzzy systems, values are indicated by a number (called a truth value) in the range from 0 to 1, where 0.0 represents absolute falseness and 1.0 represents absolute truth. While this range evokes the idea of probability, fuzzy logic and fuzzy sets operate quite differently from probability."

Lotfi Zadeh: Fuzzy logic-Incoporating Real-World Vagueness. By Pragya Agarwal. From the Center for Spatially Integrated Social Science's collection of CSISS Classics: "summaries and illustrations of major contributions to spatial thinking in the social sciences." "Fuzzy logic was first invented as a representation scheme and calculus for uncertain or vague notions. It is basically a multi-valued logic that allows more human-like interpretation and reasoning in machines by resolving intermediate categories between notations such as true/false, hot/cold etc used in Boolean logic. ... Professor Zadeh's paper on fuzzy sets introduced the concept of a class with unsharp boundaries and marked the beginning of a new direction by providing a basis for a qualitative approach to the analysis of complex systems in which linguistic rather than numerical variables are employed to describe system behavior and performance. This approach centres on building better models of human reasoning and decision-making."

Automating the Underwriting of Insurance Applications. By Kareem S. Aggour, Piero P. Bonissone, William E. Cheetham, and Richard P. Messmer. AI Magazine 27(3): Fall 2006, 36. "An end-to-end system was created at Genworth Financial to automate the underwriting of long-term care (LTC) and life insurance applications. Relying heavily on artificial intelligence techniques, the system has been in production since December 2002 and in 2004 completely automates the underwriting of 19 percent of the LTC applications. A fuzzy logic rules engine encodes the underwriter guidelines and an evolutionary algorithm optimizes the engine’s performance. Finally, a natural language parser is used to improve the coverage of the underwriting system."

Fuzzy logic - This headline is (half) false. The Economist (October 2, 2003). "Epimenides the Cretan, a philosopher of the 6th century BC , is said to have uttered the sentence, 'All Cretans are liars'. As he himself was a Cretan, this gave rise to a paradox—if he were telling the truth, then he would be a liar. Depending on how one defines a liar, the paradox is resolvable; he could have been a habitual liar who was telling the truth in this one instance. However, a stronger version of the paradox, known as the Liar paradox -- 'this sentence is false' -- is not resolvable in conventional logic systems. Indeed, the circular loop that the sentence induces -- if it is false, it must be true, and if true, false -- has been used more than once in science-fiction movies to cause marauding computers to lose their sanity and explode. But in a new paper, Kostis Vezerides of the American College of Thessaloniki, and Athanasios Kehagias of the Aristotle University of Thessaloniki, in Greece, show that, in almost all cases, paradoxes such as the Liar are resolvable with the use of 'fuzzy logic'. ... In the 1960s, Lotfi Zadeh of the University of California at Berkeley came up with the catchy innovation of 'fuzzy logic'."

Fuzzy Anti-Lock Brake System Solution. A fascinating context for an introduction to fuzzy logic. Authored by David Elting, Mohammed Fennich, Robert Kowalczyk and Bert Hellenthal, and available from Intel's Developer Site.

Fuzzy logic and neural nets: still viable after all these years? Though no longer headliners, fuzzy logic and neural networks are options in tackling challenging applications. By Graham Prophet. EDN Magazine (June 10, 2004). "[B]oth still have their place in your engineering tool kit. The two techniques are essentially unrelated, except that they both provide control methodologies to handle highly nonlinear or poorly specified problems, they both came to some prominence at about the same time, and they both faded from view in much the same way. Both neural networks and fuzzy logic aspire to allow electronic systems, built with familiar circuit techniques or employing conventional computing technologies, to attack certain problems in a way that mimics human responses and abilities. ... What happens to the expertise built up in neural and fuzzy techniques from their first flush of popularity? If you set about tracking down some of the pioneering companies from as much as a decade ago, you'd find that, although many no longer exist, some have transformed themselves into software-design and consultancy operations. These businesses are applying the same neural and fuzzy techniques but mainly in software simulation running on conventional computers, in areas such as financial modeling, financial services, and data mining."

Foreword for Dr. Hoffmann's treatise, Entwurf von Fuzzy-Reglern mit Genetischen Algorithmen. By Lotfi A. Zadeh (1996). "[F]uzzy-genetic systems fall within the province of soft computing -- a concept of computing which began to crystallize during the past decade. Essentially, soft computing (SC) is an association of computing methodologies centering on fuzzy logic (FL), neurocomputing (NC), genetic computing (GC) and probabilistic computing (PC)."

• Papers by Lotfi A. Zadeh, including Fuzzy Sets (Information and Control 8 (1965): pages 338-353), can be accessed from the homepage of BISC : the Berkeley Initiative in Soft Computing

BISC : the Berkeley Initiative in Soft Computing, Electrical Engineering and Computer Sciences Department. "The basic ideas underlying soft computing in its current incarnation have links to many earlier influences, among them Prof. Zadeh’s 1965 paper on fuzzy sets; the 1973 paper on the analysis of complex systems and decision processes; the 1976 paper on fuzzy-algorithmic approach, and the 1979 report (1981 paper) on possibility theory and soft data analysis. BISC Program is the world-leading center for basic and applied research in soft computing. The principal constituents of soft computing (SC) are fuzzy logic (FL), neural network theory (NN) and probabilistic reasoning (PR), with the latter subsuming belief networks, evolutionary computing including DNA computing, chaos theory and parts of learning theory."

• Be sure to see their page about the History of BISC during the 1990’s.

European Society for Fuzzy Logic and Technology (EUSFLAT).

FuzzyCLIPS web site from the National Research Council's Institute for Information Technology. "[A]n extension of the CLIPS (C Language Integrated Production System) expert system shell from NASA. It was developed by the Integrated Reasoning Group of the Institute for Information Technology of the National Research Council of Canada and has been widely distributed for a number of years. It enhances CLIPS by providing a fuzzy reasoning capability that is fully integrated with CLIPS facts and inference engine allowing one to represent and manipulate fuzzy facts and rules."

Fuzzy Logic resources from PCAI Magazine.

Fuzzy Logic Web Sites. An extensive collection of resources from Robert Fullér, Institute For Advanced Management Systems Research, Akademi University, Finland. Topics covered include: Professional Organizations and Networks; Fuzzy Logic Journals and Books; and Research groups.

IEEE Transactions on Fuzzy Systems, published by the IEEE Computational Intelligence Society.

Japan SOciety for Fuzzy Theory and intelligent informatics (SOFT).

North American Fuzzy Information Processing Society. Resources include links to related research groups and a collection of Toolkits/Software.

Robots in Action - Reactive Planning and Control. From SRI. "The following video clips show results of the application of fuzzy-logic techniques to the reactive control of the AIC's autonomous mobile platform: Flakey. The clips show a typical experimental run, the acquisition and fusion of perceptual information in the local perceptual space of the autonomous robot, and the activation of control structures by the intelligent controller."

Other References Offline

Advances in Fuzzy Systems -- Applications and Theory, published by World Scientific Publishing, "is a series of specialized books aiming to provide an up-to-date picture of developments in fuzzy logic, ranging from the strictly theoretical to the latest applications. Topics covered will include fuzzy mathematical theory, soft computing, hardware implementations, and industrial applications. Most books in this series will consist of collections of review articles by acknowledged experts in their field." Fuzzy Logic in Environmental Sciences: A Bibliography. "Domains of interest include: Agriculture, climatology, earthquakes, ecology, environmental sciences, fisheries, geography, geology, hydrology, meteorology, mining, natural resources, oceanography, petroleum, pollution, risk analysis, and rivers+lakes. ... We are preparing a chapter on fuzzy logic for a handbook in AI. The handbook is being assembled by AIRIES (Artificial Intelligence Research in Environmental Sciences). The book is intended to introduce environmental scientists to practical, state-of-the-art AI techniques. Many references were kindly given to us when we posted questions on newsgroups for the above-listed domains and on the met.ai newsgroup and fuzzy logic newsgroup. The AIRIES Fuzzy Team includes Rich Bankert, Mike Hadjimichael, and Bjarne Hansen."

An Introduction to Fuzzy Logic Applications in Intelligent Systems. Ronald R. Yager and Lofti A. Zadeh (Eds.). 1992. Springer Science+Business Media. "An Introduction to Fuzzy Logic Applications in Intelligent Systems consists of a collection of chapters written by leading experts in the field of fuzzy sets. Each chapter addresses an area where fuzzy sets have been applied to situations broadly related to intelligent systems."