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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