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FUZZY EXPERT SYSTEMS
The most commonly used zero-order Sugeno fuzzy model applies fuzzy rules
in the following form:
IF
AND
THEN
x is A
y is B
z is k
where k is a constant.
In this case, the output of each fuzzy rule is constant. In other words, all
consequent membership functions are represented by singleton spikes. Figure
4.15 shows the fuzzy inference process for a zero-order Sugeno model. Let us
compare Figure 4.15 with Figure 4.10. The similarity of Sugeno and Mamdani
methods is quite noticeable. The only distinction is that rule consequents are
singletons in Sugeno’s method.
How is the result, crisp output, obtained?
As you can see from Figure 4.15, the aggregation operation simply includes all
the singletons. Now we can find the weighted average (WA) of these singletons:
WA ¼
ðk1Þk1 þ ðk2Þk2 þ ðk3Þk3 0:1 20 þ 0:2 50 þ 0:5 80
¼ ¼ 65
ðk1Þþðk2Þþðk3Þ
0:1 þ 0:2 þ 0:5
Thus, a zero-order Sugeno system might be sufficient for our problem’s needs.
Fortunately, singleton output functions satisfy the requirements of a given
problem quite often.
How do we make a decision on which method to apply – Mamdani or
Sugeno?
The Mamdani method is widely accepted for capturing expert knowledge. It
allows us to describe the expertise in more intuitive, more human-like manner.
However, Mamdani-type fuzzy inference entails a substantial computational
burden. On the other hand, the Sugeno method is computationally effective and
works well with optimisation and adaptive techniques, which makes it very
attractive in control problems, particularly for dynamic nonlinear systems.
4.7 Building a fuzzy expert system
To illustrate the design of a fuzzy expert system, we will consider a problem of
operating a service centre of spare parts (Turksen et al., 1992).
A service centre keeps spare parts and repairs failed ones. A customer brings a
failed item and receives a spare of the same type. Failed parts are repaired, placed
on the shelf, and thus become spares. If the required spare is available on the
shelf, the customer takes it and leaves the service centre. However, if there is no
spare on the shelf, the customer has to wait until the needed item becomes
available. The objective here is to advise a manager of the service centre on
certain decision policies to keep the customers satisfied.