intelligence. A human will consider him to be mostly clever, above aver

age, which is exactly what can be inferred from his fuzzy set membership
values.
Ü
NOTE It’s worth noting that the linguistic terms associated with fuzzy sets
can change their meaning when used in differing frames of reference. For
example, the meaning of the fuzzy sets Tall, Medium, and Short will be different
for Europeans than it would be for the pygmies of South America. All fuzzy sets,
therefore, are defined and used within a context.
A membership function can be written in mathematical notation like this:
(10.4)
Using this notation we can write Brian’s degree of membership, or DOM
for short, in the fuzzy set Clever as:
(10.5)
Fuzzy Set Operators
Intersections, unions, and complements of fuzzy sets are possible, just as
they are with crisp sets. The fuzzy intersection operation is mathematically
equivalent to the AND operator. The result of ANDing two or more fuzzy
sets together is another fuzzy set. The fuzzy set of people who are Average
AND Clever is shown graphically in Figure 10.6.
The graphical example illustrates well how the AND operator is equivalent
to taking the minimum DOM (degree of membership) for each set a value
is a member of. This is written mathematically as:
(10.6)
Fuzzy Logic  421
Fuzzy Sets
Figure 10.6. The set of people who are Average AND Clever
__
()
Name of set
Fx
()
(115) 0.75
Brian Clever
Clever F==
{}
() min (), ()
Average Clever Average Clever
FxFxFx
Ç
=