Information Technology Reference
In-Depth Information
r i ·
inwhich the elements of the classical product of matrices (rows by columns)
1
i n
r i ,
a ij are substituted by max
1
i n T 0 (
a ij )
.
This composition is called the max- T 0 product of matrices , instead of the classical
sum-prod composition. Hence,
s 1 ,...,
s m ) =[ μ P ∗ ]↗[
[ μ Q ∗ ]= (
J
] ,
gives the CRI's output.
Example 3.4.5 With
μ P
=
0
.
7
/
x 1 +
0
.
8
/
x 2 +
1
/
x 3 ,μ Q
=
0
.
9
/
y 1 +
0
.
6
/
y 2 +
0
.
8
/
y 4 ,μ P ∗ =
0
.
6
/
x 1 +
0
.
7
/
x 2 +
1
/
x 3 ,
and J
(
a
,
b
) =
min
(
1
,
1
−
a
+
b
)
, follows:
a 11
=
J
(
0
.
7
,
0
.
9
) =
min
(
1
,
1
−
0
.
7
+
0
.
9
) =
1; a 12
=
J
(
0
.
7
,
0
.
6
) =
0
.
9; a 13
=
J
(
0
.
7
,
0
) =
0
.
3; a 14 =
J
(
0
.
7
,
0
.
8
) =
1
a 21
=
J
(
0
.
8
,
0
.
9
) =
1; a 22
=
J
(
0
.
8
,
0
.
6
) =
0
.
8; a 23
=
J
(
0
.
8
,
0
) =
0
.
2; a 24
=
J
(
0
.
8
,
0
.
8
) =
1
a 31
=
J
(
1
,
0
.
9
) =
0
.
9; a 32
=
J
(
1
,
0
.
6
) =
0
.
6; a 33
=
J
(
1
,
0
) =
0; a 34
=
J
(
1
,
0
.
8
) =
0
.
8
.
Hence,
⊛
⊞
10
.
90
.
31
⊝
⊠ = (
[ μ Q ∗ ]= (
0
.
60
.
71
) ↗
10
.
80
.
21
0
.
910
.
90
.
8
),
0
.
90
.
600
.
8
since:
(
max
(
W
(
0
.
6
,
1
),
W
(
0
.
7
,
1
),
W
(
1
,
0
.
9
)),
max
(
W
(
0
.
6
,
0
.
9
),
W
(
0
.
7
,
0
.
8
),
W
(
1
,
0
.
6
)),
max
(
W
(
0
.
6
,
0
.
3
),
W
(
0
.
7
,
0
.
2
),
W
(
1
,
0
)),
max
(
W
(
0
.
6
,
1
),
W
(
0
.
7
,
1
),
W
(
1
,
0
.
8
))) = (
max
(
0
.
6
,
0
.
7
,
0
.
9
),
max
(
1
,
1
,
0
.
6
),
max
(
0
.
9
,
0
.
9
,
0
),
(
.
,
.
,
.
)) = (
.
.
.
)
max
0
6
0
7
0
8
0
910
90
8
. That is
μ Q ∗ =
0
.
9
/
y 1 +
1
/
y 2 +
0
.
9
/
y 3 +
0
.
8
/
y 4 .
In the case
μ P is interpreted P
=
more or less big ,
μ Q is interpreted Q
=
not
is interpreted P ∗ = medium , it is possible to agree on Q ∗
very big , and
μ P ∗
=
more
or less big .
3.4.2 Inference with Several Rules
Actually, there are no systems described by a single rule. What to do when a system
is described by, at least, two rules? With, for example
•
r1: If x is P 1 , then y is Q 1
•
r2: If x is P 2 , then y is Q 2 ,
an input
μ P ∗ gives
 
Previous Page
Next Page
Fuzzy Logic: An Introductory Course for Engineering Students
Search WWH ::




Custom Search
Home