Overview
Fuzzy Subsets
A characteristic function, {% \chi_A %} is a function which indicates whether an element {% x %} is in a given set. Ie.
{% \chi_A(x) = 1 \; for \; x \in A %}
{% \chi_A(x) = 0 \; for \; x \notin A %}
Fuzzy set theory takes this definition and extends it for use in the definition of a fuzzy subset. In particular, a fuzzy
subset of a set {% A %} is defined to be the characteristic function
{% \chi : A \rightarrow [0,1] %}
where now, the range is anywhere in the interval between {% 0 %} and {% 1 %}. The function is called the membership
function for the given subset, and it indicates the degree to which {% x %} belongs to {% A %}.