Notice how each rule provides a result as a truth value of a particular membership function for the output variable.

We start by defining the input temperature states using "membership functions":

This interval can be interpreted as an extension to the fuzzy membership function.

This result in turn will be mapped into a membership function and truth value controlling the output variable.

The most typical fuzzy set membership function has the graph of a triangle.

One application of membership functions is as capacities in decision theory.

So, what does one do when there is uncertainty about the value of the membership function?

It is applied specifically to membership functions and capacities.

Let A be a fuzzy variable with a continuous membership function.

Another designer might equally well design a set membership function where the glass would be considered full for all values down to 50 ml.