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a particular value, a high resale price, with a mileage around certain mileage, comfortable and a low
maintenance cost. Such systems would work only on a specific type of products (cars in this case) if
one wishes to purchase a personal computer for example, the variables would change as is the fuzzy
logic system.
the fuzzy inference syste M
There are two concepts within fuzzy systems that play a central role in our application domain. The
first one is a linguistic variable, that is, a variable whose values are words or sentences in a natural
or synthetic language. Fuzzy set theory, which is based on such paradigm, deals with the ambiguity
found in semantics (Zadeh, 1965). The second concept is that of a fuzzy IF-THEN rules, in which the
antecedent and the consequent parts are propositions containing linguistic variables (Mamdani, 1994).
These two concepts are effectively used in the fuzzy logic controller paradigm as shown in Figure 2.
The numerical values of the inputs
i
x
∈
with
( 1,..., )
are fuzzified into linguistic values
1
F
i
=
n
F F
, ,...,
n
i
where
F
j
's are defined as fuzzy sets in the input universe of discourse
.
U U U
=
×
× ×
U
⊂ ℜ
n
1
2
n
G G G
in the output
universe of discourse
V
by using fuzzy IF-THEN rules which are defined in the rule base:
A fuzzy inference engine judges and evaluates several linguistic values
1
, ,...,
n
(1)
R IF x F and and x F Theny G
( )
j
:
∈
j
...
∈
j
∈
j
i
1
n
n
where
(
j
=
and
M
is the number of rules in the principle base. Each fuzzy IF-THEN rule in the
form of (1) defines a fuzzy set
1
1,.. )
→
in the product space
U
×
V
. Let
'
A
be an arbitrary
F F
j
×
2
...
j
× ×
F
j
G
j
n
input fuzzy set in
U
. A fuzzy set
B
m
in
V
can be calculated as:
(2)
T
( )
y
= ⊕
( ,..., )
x
x
∈
U
( ,..., )
x
x
⊗
( ,..., , )
x
x y
m
1
n
A
'
1
n
m
m
m
1
n
A R
'
F
× ×
...
F
→
G
1
n
n
Figure 2. The fuzzy logic controller
Principle
Rule Base
X
1
Fuzzy
Inference
y
X
Fuzzy sets in
V
2
Fuzzy sets in
U
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