Fuzzy Logic

Making Inferences with Imprecise Concepts

"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.

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Representation & Reasoning

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Good Starting Places

Publication

Fuzzy logic comes to life

"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."

Oct 19 2006, By Sheble, Nicholas

overview

Link

Fuzzy Logic

Video 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."

2005

Link

QuickStudy: Fuzzy Logic

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."

2004

General Readings

Link

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."

2006

Link

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 paradoxif 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'."

2003

Link

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."

2002

Link

Fuzzy Logic resources

Fuzzy Logic resources from PCAI Magazine.

collection

Link

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."

Organizations

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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."

Link

North American Fuzzy Information Processing Society

Resources include links to related research groups and a collection of Toolkits/Software.

Link

Japan Society for Fuzzy Theory and Intelligent Informatics (SOFT)

In Japanese.

Educational Resources

Video

Fuzzy Logic Tutorial

"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."

By Michael Berthold, 55 min, 2005

tutorial, tutorials, uncertainty

Link

FAQ: Fuzzy Logic and Fuzzy Expert Systems

Don't miss FAQ #2, What is Fuzzy Logic?

By Mark Kantrowitz, 1997

Link

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.

1996

course materials

Hardware and Software

Link

FuzzyCLIPS

"[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."

Journals and Proceedings

Link

IEEE Transactions on Fuzzy Systems

Published by the IEEE Computational Intelligence Society.

Videos

Video

Fuzzy Logic Tutorial

"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."

By Michael Berthold, 55 min, 2005

tutorial, tutorials, uncertainty

Classic Articles & Books

Publication

A theory of approximate reasoning

By Zadeh, L. A. , 1979

classic

Publication

Fuzzy sets as a basis for a theory of possibility

By Zadeh, L. A. , 1978

classic

Publication

Fuzzy sets

By Zadeh, L.A., 1965

classic

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