What Is Fuzzy Logic?

Fuzzy Inference Systems
Mamdani-type inference, asdefined for the toolbox, expects the output
membership functions to be fuzzy sets. After the aggregation process,
there is a fuzzy set for each output variable that needs defuzzification. It
is possible, and in many cases much more efficient, to use a single spike
as the output membership function rather than a distributed fuzzy set.
This type of output is sometimes known as a singleton output membership
function, and it can be thought of as a pre-defuzzified fuzzy set. It enhances
the efficiency of the defuzzification process because it greatly simplifies the
computation required by the more general Mamdani method, which finds the
centroid of a two-dimensional function. Rather than integrating across the
two-dimensional function to find the centroid, you use the weighted average
of a few data points. Sugeno-type systems support this type of model. In
general, Sugeno-type systems can be used to model any inference system in
which the output membership functions are either linear or constant.
Overview of Fuzzy Inference Process
This section describes the fuzzy inference process and uses the example of
the two-input, one-output, three-rule tipping problem “The Basic Tipping
Problem” on page 1-12 that you saw in the introduction in more detail. The
basic structure of this example is shown in the following diagram:
Dinner for Two
a 2 input, 1 output, 3 rule system
Input 1
Service (0-10)
Input 2
Food (0-10)
Rule 1
Rule 2
Rule 3
If service is poor or food is rancid,
then tip is cheap.
If service is good, then tip is average.
If service is excellent or food is
delicious, then tip is generous.
S
Output
Tip (5-25%)
The inputs are crisp
(non-fuzzy)
numbers limited to a
specific range.
All rules are
evaluated in parallel
using fuzzy
reasoning.
The results of the
rules are combined
and distilled
(defuzzified).
The result is a
crisp (non-fuzzy)
number.
2-21