In this example we want to describe the set of young people. More formally we can denote
B = {set of young people}
Since, in general, age starts at 0, the lower range of this set ought to
be clear. The upper range, on the other hand, is rather hard to define.
As a first attempt we set the upper range to, say, 20 years. Therefore
we get B as a crisp interval, namely:
B = [0,20]Now the question arises: why is somebody on his 20th birthday young and right on the next day not young? Obviously, this is a structural problem, for if we move the upper bound of the range from 20 to an arbitrary point we can pose the same question.
A more natural way to construct the set B would be to relax the strict separation between young and not young. We will do this by allowing not only the (crisp) decision YES s/he is in the set of young people or NO s/he is not in the set of young people but more flexible phrases like Well, s/he belongs a little bit more to the set of young people or NO, s/he belongs nearly not to the set of young people.
The next page shows how a fuzzy set allows us to define such a
notion as
s/he is a little young.
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Introduction