Information Technology Reference
In-Depth Information
Assume, that linguistic values from Table 25.1 are predefined. In general, fuzzy
relations
R
SD
and
R
SD
can be defined as follows:
R
{
o
,
c
}
SD
:
Σ
×
Δ
→ F
([
0
,
1
])
(25.4)
where
; denotes the set of all ordinary fuzzy sets that
can be defined within the universal set
F
([
0
,
1
])
is a power set of
[
0
,
1
]
[16, 17].
Each linguistic value can be defined by an expert [24]. For example, an expert
can define a fuzzy set often and supports his/her interpretation with the following
sentence: symptom/sign and disease meet each other often, if it happens in, approx-
imately, 60%. Here we deal with fuzzy relations of type II [16]. An example of
linguistic values from the Table 25.1 as trapezoidal fuzzy sets [16] is shown in the
Table 25.5.
Another possibility to define linguistic values is to assign to them an ordered set
of numbers from
[
0
,
1
]
[
0
,
1
]
as shown, e.g„ in the Table 25.3.
Table 25.3
Representation of linguistic terms as numbers
never very seldom seldom sometimes unspecified occasionally often very often always
0
0
.
2
0
.
25
0
.
4
0
.
5
0
.
6
0
.
75
0
.
8
1
.
0
Table 25.4
Representation of linguistic terms as intervals
never very seldom seldom sometimes unspecified occasionally
often
very often always
[
0
,.
2
)
(
.
2
,.
25
]
(
.
25
,.
4
]
(
.
4
,.
5
)
[
.
5
,.
5
]
(
.
5
,.
6
]
(
.
6
,.
75
]
(
.
75
,.
8
]
(
.
8
,
1
]
Table 25.5
Representation of linguistic terms as trapezoidal fuzzy sets
never
very seldom
seldom
sometimes
unspecified
(
0
,
0
,
0
,
0
.
2
)
(
0
,
0
.
0
,
0
.
2
,
0
.
25
)
(
0
.
0
,
0
.
2
,
0
.
25
,
0
.
4
) (
0
.
2
,
0
.
25
,
0
.
4
,
0
.
5
) (
.
25
,.
4
,.
5
,.
6
)
occasionally
often
very often
always
(
0
.
4
,
0
.
5
,
0
.
6
,
0
.
75
) (
0
.
5
,
0
.
6
,
0
.
75
,
0
.
8
) (
0
.
6
,
0
.
75
,
0
.
8
,
1
.
0
) (
0
.
75
,
0
.
8
,
1
.
0
,
1
.
0
)
The possibility to define the fuzzy relations as intervals (e.g., presented in the
Table 25.4) was discussed in [18]. It is based on the assumption, that different
patient settings influence all-purpose consultant systems.
Besides above described fuzzy relations
R
SD
and
R
SD
there can be another type
of a symptom/sign-disease relation due to the expert estimations, e.g., an exclusion
relation
R
SD
.Thevalue
R
SD
(
indicates the degree in which
the present symptom/sign (combination) excludes (or disconfirms) the disease
d
j
(it
is so called negative knowledge [8]). A proposal, that symptoms/signs cannot at the
same time confirm and exclude the diagnosis, may lead to the following assump-
tion:
R
SD
(
:
Σ
×
Δ
→
[
0
,
1
]
s
i
,
d
j
)
0 or (but not “and”!)
R
SD
(
0 at a given time. Notice, that
it is only one of the possible pre-definitions. For example, there might not be enough
s
i
,
d
j
)=
s
i
,
d
j
)=
