C++ Neural Networks and Fuzzy Logic:A Look at Fuzzy Logic
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C++ Neural Networks and Fuzzy Logic


(Publisher: IDG Books Worldwide, Inc.)

Author(s): Valluru B. Rao

ISBN: 1558515526

Publication Date: 06/01/95










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Sample output from the program is shown below. Our input is in italic; computer output is not. The categories defined by the graph in Figure 3.2 are entered in this example. Once the categories are set up, the first data entry of 4.0 gets fuzzified to the accommodative category. Note that the memberships are also presented in each category. The same value is entered again, and this time it gets fuzzified to the very accommodative category. For the last data entry of 12.5, you see that only the very tight category holds membership for this value. In all cases you will note that the memberships add up to 1.0.



fuzzfier

Please type in a category name, e.g. Cool
Enter one word without spaces
When you are done, type `done' :

v.accommodative

Type in the lowval, midval and highval
for each category, separated by spaces
e.g. 1.0 3.0 5.0 :

0 3 6

Please type in a category name, e.g. Cool
Enter one word without spaces
When you are done, type `done' :

accommodative

Type in the lowval, midval and highval
for each category, separated by spaces
e.g. 1.0 3.0 5.0 :

3 6 9

Please type in a category name, e.g. Cool
Enter one word without spaces
When you are done, type `done' :

tight

Type in the lowval, midval and highval
for each category, separated by spaces
e.g. 1.0 3.0 5.0 :

5 8.5 12

Please type in a category name, e.g. Cool
Enter one word without spaces
When you are done, type `done' :

v.tight

Type in the lowval, midval and highval
for each category, separated by spaces
e.g. 1.0 3.0 5.0 :

10 12 14

Please type in a category name, e.g. Cool
Enter one word without spaces
When you are done, type `done' :

done

===================================
==Fuzzifier is ready for data==
===================================

input a data value, type 0 to terminate
4.0

Output fuzzy category is ==> accommodative<==
category membership
-----------------------------
v.accommodative 0.666667
accommodative 0.333333
tight 0
v.tight 0

input a data value, type 0 to terminate
4.0

Output fuzzy category is ==> v.accommodative<==
category membership
-----------------------------
v.accommodative 0.666667
accommodative 0.333333
tight 0
v.tight 0

input a data value, type 0 to terminate
7.5

Output fuzzy category is ==> accommodative<==
category membership
-----------------------------
v.accommodative 0
accommodative 0.411765
tight 0.588235
v.tight 0

input a data value, type 0 to terminate
11.0

Output fuzzy category is ==> tight<==
category membership
-----------------------------
v.accommodative 0
accommodative 0
tight 0.363636
v.tight 0.636364

input a data value, type 0 to terminate
12.5

Output fuzzy category is ==> v.tight<==
category membership
-----------------------------
v.accommodative 0
accommodative 0
tight 0
v.tight 1

input a data value, type 0 to terminate
0
All done. Have a fuzzy day !


Fuzzy Control Systems
The most widespread use of fuzzy logic today is in fuzzy control applications. You can use fuzzy logic to make your air conditioner cool your room. Or you can design a subway system to use fuzzy logic to control the braking system for smooth and accurate stops. A control system is a closed-loop system that typically controls a machine to achieve a particular desired response, given a number of environmental inputs. A fuzzy control system is a closed-loop system that uses the process of fuzzification, as shown in the Federal Reserve policy program example, to generate fuzzy inputs to an inference engine, which is a knowledge base of actions to take. The inverse process, called defuzzification, is also used in a fuzzy control system to create crisp, real values to apply to the machine or process under control. In Japan, fuzzy controllers have been used to control many machines, including washing machines and camcorders.
Figure 3.3 shows a diagram of a fuzzy control system. The major parts of this closed-loop system are:

Figure 3.3  Diagram of a fuzzy control system.

•  machine under control—this is the machine or process that you are controlling, for example, a washing machine
•  outputs—these are the measured response behaviors of your machine, for example, the temperature of the water
•  fuzzy outputs—these are the same outputs passed through a fuzzifier, for example, hot or very cold
•  inference engine/fuzzy rule base—an inference engine converts fuzzy outputs to actions to take by accessing fuzzy rules in a fuzzy rule base. An example of a fuzzy rule: IF the output is very cold, THEN increase the water temperature setting by a very large amount
•  fuzzy inputs—these are the fuzzy actions to perform, such as increase the water temperature setting by a very large amount
•  inputs—these are the (crisp) dials on the machine to control its behavior, for example, water temperature setting = 3.423, converted from fuzzy inputs with a defuzzifier

The key to development of a fuzzy control system is to iteratively construct a fuzzy rule base that yields the desired response from your machine. You construct these fuzzy rules from knowledge about the problem. In many cases this is very intuitive and gives you a robust control system in a very short amount of time.




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