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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
.
.
 
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