Information Technology Reference
In-Depth Information
Table
25.10
Linguistic
and
numerical
descriptions
of
a
rare
disease
Primary
Ciliary Diskinesia
Primary Ciliary Diskinesia
d
3
.
wheezing
often
0
75
breathlessness
0
.
75
often
anosmia
0
.
75
often
f ever
0
.
75
often
sinusitis
0
.
8
very often
chronic otitis
0
.
75
often
⎧
⎨
⎫
⎬
min
{
0
.
4
,
0
.
4
}
min
{
0
.
2
,
0
.
2
}
min
{
0
.
25
,
0
.
25
}
D
p
(
d
1
)=
max
=
0
.
4
(25.11)
{
.
,
.
}
⎩
min
0
4
0
4
⎭
{
.
,
.
}
min
0
4
0
4
{
.
,
.
}
min
0
25
0
25
−
This standard max
min composition in our case guarantees that the degree of oc-
currence can be less than 0
4, but not more. If we take the absolute difference (for
two numbers
a
and
b
their absolute difference is defined as
.
) instead of min-
operation (max-operation remains unchanged) we obtain more flexibility to detect
deviations. For example, for
S
p
the membership degree of
d
1
in this case is 0 and for
S
p
we obtain 0
|
a
−
b
|
8. If instead of the
max
operator we take another aggregation opera-
tor, such as the arithmetic mean of deviations (the arithmetic mean of
a
1
,
.
a
2
,...,
a
n
a
1
+
a
2
+
···
+
a
n
n
), for
d
1
in the case of
S
p
we obtain 0 as well and 0
is
3inthecase
of
S
p
. We interpret 0 as a sign of most believable diagnosis, and every deviation
from 0 points less believable diagnosis. The question is, as always in applications,
how to detect a threshold, under (or above) which a suspicious of the RD arises. If
we take
max
-absolute difference composition of
S
p
and
R
SD
and a result is differ-
ent from 0, the final value shows that at least one symptom/sign differs from the
normal case, but does not say anything about the rest of symptoms. When the RD
can be pointed by a representative symptom (i.e., such symptom which presence/ab-
sence is a sure sign of the non-normality of a diagnosis, as was mentioned above,
outstanding symptoms/signs) max- absolute difference is suitable.
The
mean
-absolutedifference composition of
S
p
and
R
SD
shows the mean value
of all deviations. As it is often with RDs, they are described with the same symp-
toms/signs as “normal” diseases and only a certain deviation can point the RD, the
application of
mean
-absolute difference composition of
S
p
and
R
SD
seems to be
reasonable. Notice, that in general,
p
.
−
mean
and/or other distance metrics can be
considered.
We can also instead of absolute difference operation consider
prod
operation.
