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we assume that a state of an investigated patient is described with the same linguistic
values (Table 25.1) as
S
−
D
relationships, practically often only three of them are
used: always (yes),never(no) and unspecified.
25.3.3
The Inference Mechanism
Amax
min composition of fuzzy relations [26, 32] or its generalised version
t
-
conorm-
t
-norm composition can be used for medical diagnosing. Thus,
−
D
p
=
def
S
p
◦
R
SD
(25.5)
is a composition of a fuzzy set and a fuzzy relation and
∀
d
j
∈
Δ
D
p
(
d
j
)=
def
s
i
∈
Σ
∧{
∨
S
p
(
s
i
)
;
R
SD
(
s
i
,
d
j
)
}
(25.6)
Δ
→
[
,
]
∨
where
D
p
:
0
1
are inferred possible diagnoses for the patient and
is a
∧
t
-conorm,
is a
t
-norm.
In general, the aggregation operators can be used in this inference mechanism
[16].
25.3.4
Interpretation of Inference Results
As can be seen from Section 25.3.3, we have obtained a fuzzy set
D
p
and with each
d
j
its membership degree is associated. An appropriate defuzzyfication method
allows us to choose the reliable diagnosis. It is one way.
Another possibility (“because of features of physicians' thinking” [4, 8]) is to
differentiate in advance several types of inference rules/compositions for a final
diagnosis, e.g.,:
confirmation (by present symptoms/signs):
D
p
=
def
S
p
◦
R
SD
,
•
exclusion (by present symptoms/signs):
D
p
=
def
S
p
◦
(
R
SD
)
•
1
−
,
exclusion (by absent symptoms/signs):
D
p
=
def
(
R
SD
,
•
1
−
S
p
)
◦
possible (by present symptoms/signs):
D
p
=
R
SD
,
•
def
S
p
◦
possible (by present symptoms/signs):
D
p
=
def
S
p
◦
R
t
SD
,
•
R
SD
The results for different types of a symptom/sign-disease relation have to be inter-
preted for obtaining the patient(s) diagnosis. For example, a diagnosis
d
i
is con-
firmed (by
D
p
) iff there exists a fully present symptom/sign
s
j
(
S
p
exclusion (by present symptoms/signs):
D
p
=
•
◦
def
S
p
(
s
j
)=
1) which
has full/maximal contribution to the diagnosis, i.e.,
R
SD
(
1. A diagnosis
d
i
is excluded by a present symptom/sign (by
D
p
) iff there exists a fully present symp-
tom/sign
s
j
(
S
p
(
s
j
,
d
i
)=
s
j
)=
1) which has 0 (i.e. negative) contribution to the diagnosis,
i.e.,
R
SD
(
0. A diagnosis
d
i
is excluded by an absent symptom/sign (by
D
p
)
iff there exists a fully absent symptom/sign
s
j
(
S
p
(
s
j
,
d
i
)=
s
j
)=
0) which has full/maximal
occurrence for the diagnosis, i.e.,
R
SD
(
s
j
,
d
i
)=
1.
