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In-Depth Information
1
Let
Example 4.2.1
•
X
={
p
1
,...,
p
4
}
, a set of patients
•
Y
={
s
1
,
s
2
,
s
3
}
, a set of symptoms
•
Z
={
d
1
,...,
d
5
}
, a set of deceases,
and the fuzzy relation
˃
⊛
⊞
0
.
7000
.
30
.
6
⊝
⊠
[
˃
]=
0
.
50
.
50
.
80
.
40
00
.
70
.
20
.
90
showing the medical knowledge of how strongly each symptom is associated with a
decease. Suppose also that, by examining the patients, the doctors conclude thematrix
⊛
⊞
00
.
30
.
4
⊝
⊠
0
.
20
.
50
.
3
[
μ
]=
0
.
800
0
.
70
.
70
.
9
that describes numerically how strongly the symptoms are manifested in the patients.
Then,
[
ʻ
]=[
μ
]↗
min
[
˃
]
is the matrix expressing the association patients/deceases, and facilitates a medical
diagnose. That is,
⊛
⊝
⊞
⊠
↗
min
⊛
⊞
00
.
30
.
4
.
.
.
0
7000
30
6
.
.
.
0
20
50
3
⊝
⊠
.
.
.
.
[
ʻ
]=
0
50
50
80
40
.
0
800
00
.
70
.
20
.
90
0
.
70
.
70
.
9
⊛
⊞
0
.
30
.
40
.
30
.
40
⊝
⊠
,
0
.
50
.
50
.
50
.
40
.
2
=
0
.
7000
.
30
.
6
0
.
70
.
70
.
70
.
90
.
6
where, for instance,
t
43
=
max
(
min
(
0
.
7
,
0
),
min
(
0
.
7
,
0
.
8
),
min
(
0
.
9
,
0
.
2
))
=
max
(
0
,
0
.
7
,
0
.
2
)
=
0
.
7
.
The matrix
[
ʻ
]
results from a mixing between knowledge and observation.
1
From, Fuzzy Set Theory, by G.J. Klir, U.H. St. Clair, B. Yuan, Prentice/Hall, N.J., 1997.
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