Image Processing Reference
In-Depth Information
and
α
as the degree of truth of
x
is
A
,
β
as the degree of truth of
y
is
B
,
γ
as the
degree of truth of
z
is
C
. The rule's degree of truth (or of satisfaction) is obtained by
combining the fuzzy connectors defined above:
Imp
t
(
α, β
)
,γ
,
[8.90]
hence:
T
c
T
(
α, β
)
,γ
.
[8.91]
Likewise for the rule:
IF
(
x
is
A
OR
y
is
B
)
THEN
z
is
C
its degree of satisfaction is:
Imp
T
(
α, β
)
,γ
=
T
c
T
(
α, β
)
,γ
.
[8.92]
These rules can be used to describe in a qualitative fashion the graph of a fuzzy
function using a small number of rules. For example, a function such as that in Figure
8.12 can be described, on a rather crude granularity level, by:
IF
X
is small
THEN
Y
is small
IF
X
is medium
THEN
Y
is large
IF
X
is large
THEN
Y
is small
These rules rely on the concept of linguistic variables, discussed above, and the
semantics of the values “small”, “medium”, “large”, are defined by fuzzy sets over the
definition domains of
X
and
Y
.
Figure 8.12.
An example of a function's graph
Fuzzy rule systems have been used in many fields, essentially in fuzzy control, but
also for fuzzy reasoning, for modeling flexible criteria in image processing and fusion,
etc.
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