Databases Reference
In-Depth Information
[6]
A
=[8]
A
=[(
Temperature,normal
)]
∩
[(
Headache,yes
)]
∩
[(
Nausea,
no
]=
,
[7]
A
=[(
Temperature,normal
)]
{
6
,
8
}
∩
[(
Headache,no
]
∩
[(
Nausea,yes
)] =
{
7
}
.
3 Incomplete Data: Characteristic Sets
and Characteristic Relations
For data sets with missing attribute values, the corresponding function
ρ
is
incompletely specified (partial). A decision table with incompletely specified
function? will be called
incompletely specified
,or
incomplete
.
In the sequel we will assume that all decision values are specified, i.e.,
they are not missing. Also, we will assume that all missing attribute values
are denoted by “?”, by “*” or by “-”, lost values will be denoted by “?”, “do
not care” conditions will be denoted by “*”, and attribute-concept values by
“-”. Additionally, we will assume that for each case at least one attribute
value is specified.
Incomplete decision tables are described by characteristic relations instead
of indiscernibility relations. Also, elementary sets are replaced by characteris-
tic sets. The characteristic set was called a (binary) neighborhood in [16-18].
An example of an incomplete table is presented in Table 2.
For incomplete decision tables the definition of a block of an attribute-
value pair must be modified.
•
If an attribute
a
there exists a case
x
such that
ρ
(
x,a
) = ?, i.e., the corre-
sponding value is lost, then the case
x
should not be included in any block
[(
a,v
)] for all values
v
of attribute
a
.
•
If for an attribute
a
there exists a case
x
such that the corresponding value
is a “do not care” condition, i.e.,
ρ
(
x,a
)=
, then the corresponding case
x
should be included in blocks [(
a,v
)] for all specified values
v
of attribute
a
.
∗
Tabl e 2 .
An incomplete decision table
Attributes
Decision
Case
Temperature
Headache
Nausea
Flu
1
High
-
No
Yes
2
Very high
Yes
Yes
Yes
3
?
No
No
No
4
High
Yes
Yes
Yes
5
High
?
Yes
No
6
Normal
Yes
No
No
7
Normal
No
Yes
No
8
-
Yes
*
Yes
