What is a Fuzzy Set?
(Continued)
As stated in the introduction we want to use fuzzy sets to make computers
smarter, we now have to code the above idea more formally. In our first
example we coded all the elements of the Universe of Discourse with
0 or 1. A straight way to generalize this concept is to allow more values
between 0 and 1. In fact, we even allow infinite many alternatives between
0 and 1, namely the unit interval
I = [0, 1].
The interpretation of the numbers now assigned to all elements
of the Universe of Discourse is much more difficult. Of course, again the
number 1 assigned to an element means that the element is in the set B
and 0 means that the element is definitely not in the set B. All
other values mean a gradual membership to the set B.
To be more concrete we now show the set of young people similar
to our first example graphically by its characteristic function.
This way a 25 year old person would still be young to a degree
of 50 percent.
Java applet for fuzzy truth
Soccer football example without truth tables
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