Internet-Publication. — (Tutorial). 32 p. English.This is a series of six articles intended to share information and experience in the realm of fuzzy logic (FL) and its application (Part 1-6), by Steven D. Kaehler.This is the first in a series of six articles intended to share information and experience in the realm of fuzzy logic (FL) and its application. This article will introduce FL. Through the course of this article series, a simple implementation will be explained in detail. Each article will include additional outside resource references for interested readers.
Introduction.
Where did Fuzzy Logic Come from?
What is Fuzzy Logic?
How is FL Different from Conventional Control Methods?
How Does FL Work?
Summary.
References.This is the second in a series of six articles intended to share information and experience in the realm of fuzzy logic (FL) and its application. This article will continue the introduction with a more detailed look at how one might use FL. A simple implementation will be explained in detail beginning in the next article. Accompanying outside references are included for interested readers. In the last article, FL was introduced and the thrust of this article series presented. The origin of FL was shared and an introduction to some of the basic concepts of FL was presented. We will now look a little deeper.
Introduction.
Why Use FL?
How is FL Used?
Linguistic Variables.
Summary.
References.This is the third in a series of six articles intended to share information and experience in the realm of fuzzy logic (FL) and its application. This article and the three to follow will take a more detailed look at how FL works by walking through a simple example. Informational references are included at the end of this article for interested readers.
Introduction.
The Rule Matrix.
Starting the Process.
What is Being Controlled and How:
Summary.
References.This is the fourth in a series of six articles intended to share information and experience in the realm of fuzzy logic (FL) and its application. This article will continue the example from Part 3 by introducing membership functions and explaining how they work. The next two articles will examine FL inference and defuzzification processes and how they work. For further information, several general references are included at the end of this article.
Introduction.
Membership Functions.
Error & Error-dot Function Membership.
Summary.
References.This is the fifth in a series of six articles intended to share information and experience in the realm of fuzzy logic (FL) and its application. This article will continue the tutorial discussion on FL by looking at the output membership function and several inference processes. The next article will wrap up the discussion of the ongoing example. To further explore the topic of FL, references are included for interested readers.
In the last article, we left off with the inference engine producing fuzzy output response magnitudes for each of the effective rules. These must be processed and combined in some manner to produce a single, crisp (defuzzified) output.
Introduction.
Putting it all Together.
Input Degree of Membership.
References.This is the sixth and final article in a series intended to share information and experience in the realm of fuzzy logic (FL) and its application. This article will conclude the tutorial discussion of the ongoing FL example. For the interested reader, informational references are included.
Introduction.
Inferencing.
Defuzzification - Gettung Back to Crisp Numbers.
A "Fuzzy Centroid" Algorithm.
Tuning and System Enhancement.
Summary.
Conclusion.
References.Example Illustrations (To Case 1-5).
The following five cases show what the system computes as error decreases toward zero and then changes to a positive value. Pictures of the input and output membership functions are included. The rate-of-change of the error stays constant throughout the five cases. It is not likely that this would happen in a real system, but for purposes of this illustration, that case has been assumed. The values of error and error-dot indicated from the membership functions are plugged into the rulebase from the "KEY" below and the responses computed for each case. These responses are then mathematically combined to yield a crisp output.
Note that because the "zero" membership function is centered on zero in the output function, its influence in the output computation is only in the denominator. The center of the "zero" doesn't need to be at zero, it just happens to be in this example..
