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used. For example,
Δ
can denote more typical child/adolescence diseases in Geor-
gia,
Σ
are symptoms/signs of these diseases, and
Π
are investigated patients for the
diseases.
It is a formalized representation of the fuzzy IF-THEN rules mentioned above.
For example, two types of symptom/sign-disease relations -confirmation
R
SD
and
occurrence
R
SD
relations - can be used in the knowledge base of a system [4, 8].
These fuzzy relations estimate each symptom/sign-diagnose connection from two
perspectives: strength of confirmation (the degree to which a symptom/sign
S
con-
firmsthepresenceofdisease
D
) and frequency of occurrence of symptom/sign
S
with disease
D
.
These relations can be defined as follows.
R
SD
(
and
R
SD
(
s
i
,
d
j
)
s
i
,
d
j
)
are derived from relative frequencies, i.e., numerically
[8]:
R
SD
(
s
i
,
d
j
)=
f
(
s
i
|
d
j
)
(25.2)
and
R
SD
(
s
i
,
d
j
)=
f
(
d
j
|
s
i
)
(25.3)
f
(
d
j
∩
s
i
)
f
f
(
d
j
∩
s
i
)
f
where
f
(
s
i
|
d
j
)=
,
f
(
d
j
|
s
i
)=
;
f
(
s
i
|
d
j
)
is a conditional frequency
(
d
j
)
(
s
i
)
of
s
i
given
d
j
,
f
(
d
j
|
s
i
)
is a conditional frequency of
d
j
given
s
i
,
f
(
d
j
∩
s
i
)
is the
absolute frequency of joint occurrence of
d
j
and
s
i
,
f
are absolute
frequencies of
d
j
and
s
i
, correspondingly. We call this numerical interpretation.
A linguistic way opens a possibility to estimate relations occurrence and con-
firmation
R
SD
and
R
SD
(linguistic variables) using fuzzy sets (values of linguistic
variables), e.g., presented in the Table 25.1.
(
d
j
)
and
f
(
s
i
)
Table 25.1
Linguistic values
never very seldom seldom
sometimes unspecified
occasionally
often
very often
always
.Anex-
ample of a linguistic description of symptom/sign - disease connection is presented
in the Table 25.2. Additionally we assume that a negation of a fuzzy set is defined
as usual, e.g.,
not o f ten
The fuzzy sets (Table 25.1) are defined as mappings from
[
0
,
1
]
to
[
0
,
1
]
(
x
)=
1
−
often
(
x
)
,
x
∈
[
0
,
1
]
.
Table 25.2
Linguistic representation of symptom/sign - disease connections
d
1
d
2
...
d
n
s
1
often always
...
never
s
2
never often
...
always
.
.
s
m
often seldom
...
always
.
.