Date: 04/26/97 at 03:30:06 From: Nicholas Graham Subject: Fuzzy logic My calculus teacher suggested that when I get onto the Internet, I look up Dr. Math and ask about fuzzy logic. He said the reply would be interesting. Well, here I am asking. Thank you! Nick Graham, Grade 11 Calculus Student
Date: 04/26/97 at 10:07:53 From: Doctor Sarah Subject: Re: Fuzzy logic Hi Nick - Let's get you started exploring the internet. Using Altavista http://altavista.digital.com/ to search for "fuzzy logic" (we recommend that you use a searcher for a topic like this, since there's lots on the Web about it!) here are just a few examples of what you can find: (1) Fuzzy logic basics http://www.austinlinks.com/Fuzzy/basics.html "Fuzzy Logic is a departure from classical two-valued sets and logic, that uses "soft" linguistic (e.g. large, hot, tall) system variables and a continuous range of truth values in the interval [0,1], rather than strict binary (True or False) decisions and assignments. Formally, fuzzy logic is a structured, model-free estimator that approximates a function through linguistic input/output associations. Fuzzy rule-based systems apply these methods to solve many types of "real-world" problems, especially where a system is difficult to model, is controlled by a human operator or expert, or where ambiguity or vagueness is common. A typical fuzzy system consists of a rule base, membership functions, and an inference procedure" (2) Fuzzy logic http://cthulhu.control.com/alist/archive.old/msg01117.html "Fuzzy logic is simply described as conventional boolean logic, without the restriction that all variables must be either 0 or 1. In order for this to be meaningful, the basic boolean operators (AND, OR, and NOT), are redefined such that they can take inputs between zero and one, and can generate outputs between zero and one. There are many ways in which this can be done, but generally it is one of two ways" (3) Applications of fuzzy logic http://www.flll.uni-linz.ac.at/navigation/main_navigation/frame_whatisfuzzy.html "Automatic control of dam gates for hydroelectric-powerplants, simplified control of robots, camera aiming for the telecast of sporting events, substitution of an expert for the assessment of stock exchange activities, preventing unwanted temperature fluctuations in air-conditioning systems, efficient and stable control of car-engines, cruise-control for automobiles" and much, much more! Here's an item culled by Kevin Brown from a usenet newsgroup posting: http://www.mathpages.com/home/kmath123.htm "There is a company called OMRON Electronics, Inc, that produces a wide variety of control systems for industrial and commercial products, and they are considered a leading proponent of "fuzzy" control technology. Their literature includes a very readable 22-page document entitled "Fuzzy Logic, A 21st Century Technology: An Introduction to Fuzzy Logic and Its Application in Control Systems". I recommend it to anyone wanting a forthright explanation of how "fuzzy logic" is actually implemented in a practical control system..." This is an excellent topic to attack by doing some web (or other) research and then asking us a specific K12 level question. Does this help? -Doctor Sarah, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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