What is a Fuzzy Set?
The very basic notion of fuzzy systems is a Fuzzy (sub)set.
In classical mathematics we are familiar with what we call crisp
sets.
Here is an example:
First we consider a set X of all real numbers between 0 and 10 which
we call the universe of discourse. Now, let's define a subset A
of X of all real-numbers in the range between 5 and 8.
A = [5,8]
We now show the set A by its characteristic function, i.e., this
function assigns a number 1 or 0 to each element in X, depending
on whether the element is in the subset A or not. This results in
the following figure:
We can interpret the elements which have assigned the number 1 as
The
elements are in the set A and the elements which have assigned the
number 0 as The elements are not in the set A.
This concept is sufficient for many areas of applications. But
we can easily find situations where it lacks in flexibility. In order to
show this consider the following example:
Introduction
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