22-05-2012, 05:09 PM
FUZZY LOGIC
[attachment=22777]
THEORY
Welcome to the wonderful world of fuzzy logic, the science you can use to powerfully get things done. Add the ability to utilize personal computer based fuzzy logic analysis and control to your technical and management skills and you can do things that humans and machines cannot otherwise do. Get a competitive edge!
Following is the base on which fuzzy logic is built:
As the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, eventually arriving at a point of complexity where the fuzzy logic method born in humans is the only way to get at the problem.
WHERE DID FUZZY LOGIC COME FROM?
The concept of Fuzzy Logic (FL) was conceived by the term "fuzzy" was first used by Dr. Lotfi Zadeh in the engineering journal, "Proceedings of the IRE," a leading engineering journal, in 1962. Dr. Zadeh became, in 1963, the Chairman of the Electrical Engineering department of the University of California at Berkeley. That is about as high as you can go in the electrical engineering field. Dr. Zadeh’s thoughts are not to be taken lightly and presented not as a control methodology, but as a way of processing data by allowing partial set membership rather than crisp set membership or non-membership. This approach to set theory was not applied to control systems until the 70's due to insufficient small-computer capability prior to that time. Professor Zadeh reasoned that people do not require precise, numerical information input, and yet they are capable of highly adaptive control. If feedback controllers could be programmed to accept noisy, imprecise input, they would be much more effective and perhaps easier to implement. Unfortunately, U.S. manufacturers have not been so quick to embrace this technology while the Europeans and Japanese have been aggressively building real products around it.
FUZZY LOGIC ANALYSIS AND CONTROL
A major contributor to Homo sapiens success and dominance of this planet is our innate ability to exercise analysis and control based on the fuzzy logic method. Here is an example:
Suppose you are driving down a typical, two ways, 6 lane streets in a large city, one mile between signal lights. The speed limit is posted at 45 Mph. It is usually optimum and safest to "drive with the traffic," which will usually be going about 45 Mph. How do you define with specific, precise instructions "driving with the traffic?" It is difficult. But, it is the kind of thing humans do every day and do well.
There will be some drivers weaving in and out and going more than 45 Mph and a few drivers driving less than 45 Mph. But, most drivers will be driving 45 Mph. They do this by exercising "fuzzy logic" - receiving a large number of fuzzy inputs, somehow evaluating all the inputs in their human brains and summarizing, weighting and averaging all these inputs to yield an optimum output decision. Inputs being evaluated may include several images and considerations such as: What are the cars in front doing? How fast are they driving? Any drivers going real slow? Any trucks holding up one of the lanes? How about side traffic entering from side streets. What do you see in the rear view mirror? Even with all this, and more, to think about, those who are driving with the traffic will all be going along together at very nearly the same speed?
The Fuzzy Logic Method
The fuzzy logic analysis and control method is, therefore:
1. Receiving of one, or a large number, of measurement or other assessment of conditions existing in some system we wish to analyze or control.
2. Processing all these inputs according to human based, fuzzy "If-Then" rules, which can be expressed in plain language words.
3. Averaging and weighting the resulting outputs from all the individual rules into one single output decision or signal which decides what to do or tells a controlled system what to do. The output signal eventually arrived at is a precise appearing, defuzzified, "crisp" value.
[attachment=22777]
THEORY
Welcome to the wonderful world of fuzzy logic, the science you can use to powerfully get things done. Add the ability to utilize personal computer based fuzzy logic analysis and control to your technical and management skills and you can do things that humans and machines cannot otherwise do. Get a competitive edge!
Following is the base on which fuzzy logic is built:
As the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, eventually arriving at a point of complexity where the fuzzy logic method born in humans is the only way to get at the problem.
WHERE DID FUZZY LOGIC COME FROM?
The concept of Fuzzy Logic (FL) was conceived by the term "fuzzy" was first used by Dr. Lotfi Zadeh in the engineering journal, "Proceedings of the IRE," a leading engineering journal, in 1962. Dr. Zadeh became, in 1963, the Chairman of the Electrical Engineering department of the University of California at Berkeley. That is about as high as you can go in the electrical engineering field. Dr. Zadeh’s thoughts are not to be taken lightly and presented not as a control methodology, but as a way of processing data by allowing partial set membership rather than crisp set membership or non-membership. This approach to set theory was not applied to control systems until the 70's due to insufficient small-computer capability prior to that time. Professor Zadeh reasoned that people do not require precise, numerical information input, and yet they are capable of highly adaptive control. If feedback controllers could be programmed to accept noisy, imprecise input, they would be much more effective and perhaps easier to implement. Unfortunately, U.S. manufacturers have not been so quick to embrace this technology while the Europeans and Japanese have been aggressively building real products around it.
FUZZY LOGIC ANALYSIS AND CONTROL
A major contributor to Homo sapiens success and dominance of this planet is our innate ability to exercise analysis and control based on the fuzzy logic method. Here is an example:
Suppose you are driving down a typical, two ways, 6 lane streets in a large city, one mile between signal lights. The speed limit is posted at 45 Mph. It is usually optimum and safest to "drive with the traffic," which will usually be going about 45 Mph. How do you define with specific, precise instructions "driving with the traffic?" It is difficult. But, it is the kind of thing humans do every day and do well.
There will be some drivers weaving in and out and going more than 45 Mph and a few drivers driving less than 45 Mph. But, most drivers will be driving 45 Mph. They do this by exercising "fuzzy logic" - receiving a large number of fuzzy inputs, somehow evaluating all the inputs in their human brains and summarizing, weighting and averaging all these inputs to yield an optimum output decision. Inputs being evaluated may include several images and considerations such as: What are the cars in front doing? How fast are they driving? Any drivers going real slow? Any trucks holding up one of the lanes? How about side traffic entering from side streets. What do you see in the rear view mirror? Even with all this, and more, to think about, those who are driving with the traffic will all be going along together at very nearly the same speed?
The Fuzzy Logic Method
The fuzzy logic analysis and control method is, therefore:
1. Receiving of one, or a large number, of measurement or other assessment of conditions existing in some system we wish to analyze or control.
2. Processing all these inputs according to human based, fuzzy "If-Then" rules, which can be expressed in plain language words.
3. Averaging and weighting the resulting outputs from all the individual rules into one single output decision or signal which decides what to do or tells a controlled system what to do. The output signal eventually arrived at is a precise appearing, defuzzified, "crisp" value.