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In-Depth Information
R
SD
) from
three perspectives (confirmed, excluded, possible) just defined in this section, de-
pends on the choice of a designer. In general, it can be also accepted degrees of
exclusion or confirmation, i.e., the reals between 0 and 1.
If
Note, that an estimation of each diagnosis (under the presence of
R
SD
,
R
SD
an
exclusion
relation
is
defined
then
an
excluded
diagnosis:
D
p
=
def
S
p
◦
R
SD
.
The final diagnosis (a total degree) under the presence of the exclusion relation
can be calculated as follows:
D
tot
p
d
j
)=
def
D
p
(
D
p
(
(
d
j
)
⊕−
d
j
)
(25.7)
where
is a group operation with particular properties [8, 12]. Thus, for every
diagnosis its confirmation is decreased according to its exclusion, represented as
negative confirmation. Notice, that the group operator
⊕
⊕
is defined on
[
−
1
,
1
]
and it
should be used in accordance with definition of fuzzy relations on
.
Another possibility, we may include in our set of possible diagnostic hypotheses
for patient
p
any diseases
d
j
j
[
0
,
1
]
=
1
,...,
n
such that inequality
D
p
(
D
p
(
0
.
5
<
max
{
d
j
)
,
d
j
)
}
(25.8)
is satisfied.
Let us summarize. Several possibilities to infer a diagnosis have been described
above: first, a diagnosis can be chosen by a defuzzyfication method from (25.6);
second, all
d
j
∈
Δ
can be classified in the following classes - confirmed, excluded,
and possible - and, third, a total degree can be found due to (25.7), where each
element of the fuzzy set
D
p
shows to which degree it is true, that a patient
p
has
disease
d
j
.
25.4
How to Suspect a Rare Disease
Working with a decision-support system, a physician expects from a computer pro-
gram a tip, a help, what diagnosis it can be for a patient at hand. In this way, the
system should alarm if some things are outside of its normal functioning, i.e., if the
case is neither confirmed nor possible, for example; or, the total degree from (25.7)
has “strange” values, or (25.8) is not satisfied. Thus, such behaviour of a system
could be considered as a sign of a possible RD.
Our approach is based on the assumption, that to be able to suspect the RD, the
computer program should fix deviations from the “normal”(typical) case. For ex-
ample, one patient was diagnosed “Gastroesophageal reflux”, and another patient
was assigned with the diagnosis “Acute poststreptococcal Glomerulonephritis”. But
a physician hesitated about the diagnoses. Then a physician asked a computer sys-
tem to estimate deviations from the “normal case”, presented in the knowledge base
(Table 25.6, Table 25.7) relatively to the exhibition of patient's symptoms/signs. If
the estimation (as a result of applying the inference procedure described in the pre-
vious sections) showed, that a case in hand was excluded, or, neither confirmed nor
