Fuzzy Logic

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/