What is a Fuzzy Set?

(Continued)


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