Chapter 3
FUZZY LOGIC FOR
CONTROL
In this chapter, we set forth the basic mathematical ideas used in fuzzy control.
These ideas are illustrated here with simple examples. Their applications will
beexpandeduponinlaterchapters.
3.1 Fuzzinessandlinguisticrules
There is an inherent impreciseness present in our natural language when we
describe phenomena that do not have sharply defined boundaries. Such state-
ments as ìMary is smartî and ìMartha is youngî are simple examples. Fuzzy
sets are mathematical objects modeling this impreciseness.
Our main concern is representing, manipulating, and drawing inferences
from such imprecise statements. Fuzzy set theory provides mathematical tools
for carrying out approximate reasoning processes when available information
is uncertain, incomplete, imprecise, or vague. By using the concept of degrees
of membership to give a mathematical definition of fuzzy sets, we increase the
number of circumstances encountered in human reasoning that can be subjected
to scientific investigation.
Humans do many things that can be classified as control. Examples include
riding a bicycle, hitting a ball with a bat, and kicking a football through the
goalposts. How do we do these things? We do not have the benefitofprecise
measurements, or a system of differential equations, to tell us how to control
our motion, but humans can nevertheless become very skillful at carrying out
very complicated tasks. One explanation is that we learn through experience,
common sense, and coaching to follow an untold number of basic rules of the
form ìIf...then...î:
If the bicycle leans to the right, then turn the wheel to the right.
If the ball is coming fast, then swing the bat soon.