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If the dependency degrees of condition attributes are known and the decision
table is inconsistent (the degree of dependency is less than 1), then the table can
be decomposed to two tables according to proposition 11.9: one table is totally
inconsistent, whose dependency degree is 0; the other table is totally consistent,
whose dependency degree is 1. Certainly, only when the dependency degree is
more than 0 and less than 1, the decomposition can be processed.
The steps of reduction are as follows:
(1) Reduce a condition attribute in the decision table, that is, delete a column
from the decision table;
(2) Delete the reduplicate rows;
(3) Delete the redundant values in each decision rule.
Note, comparing with the description of knowledge representation system, the
rows here do not represent any real objects. Therefore, if two rows represent the
same decision, one of them can be deleted.
The decision table after reduction is an incomplete decision table. It only
contains the values of condition attributes that are necessary in decision making.
However, it possesses all the knowledge of original knowledge system.
1
.
Reduction of Condition Attributes
With the form of discernibility matrix, A. Skowron proposed a knowledge
representation method. Because the calculation of cores, reducts and etc with the
method is simple, the method has a lot of merits. The main idea of the method is
as follows.
Suppose
S
=(
U, A
) is a knowledge representation system,
U
={
x 1 ,x 2 ,…,x n } and
A
={
a 1 , a 2 , …, a m }, where
x i is the discussed object (
i
=1, 2, …, n) and
a j is the
attribute of objects (
).
The discernibility matrix of knowledge representation system
j
=1,2,…,
m
S
is denoted as
M(S)=[
c ij ] n×n , and the elements of the matrix are defined as:
c ij ={
a A a
(
x i ) ¬ a
(
x j ) i,j
=1,2,…,
n
}.
x j do not have. Using discernibility
matrix, it is easy to calculate the core and reduction of attribute set A.
In discernibility matrix, core is the set of elements that have only one attribute,
that is
CORE(
Thus,
c ij is the set of attributes that
x i or
A
)={
a A c ij =(
a
)for some
i, j
}
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