Chapter 9
Data Analysis
CS267
By Anand Sivaramakrishnan
A Decision table is defined as follows
T = (U,A,C,D)
where U = universe
A = set of actions
C = condition attributes
D = decision attributes
C,D is subset of A
Core is a condition attribute value which is
indispensable that means it is that value that has
direct impact on the value of decision attribute.
Reduct is a decision rule which must satisfy
following conditions
1. The rule must be true or consistent.
2. Predecessor of rule must be independent.
To simplify the decision table
Removal of unnecessary or superfluous
Follow these steps.
1. Removing redundancy.
2. Checking functional dependency/ Removing
superfluous attributes.
3. Categorizing the decisions into decision
classes
4. Find core values of all decision rules.
5. Find the value reducts of each decision rule.
Table 1
After removing all the redundant decision rules we get table 2
Table 2
• After removing attribute ‘a’
Table 3
• Therefore attribute ‘a’ is indispensable.
Removing attribute ‘b’
Table 4
• This means that after removing attribute ‘b’
the table remains consistent.
• That means attribute ‘b’ is a superfluous
attribute
• It is dispensable.
After removing attribute ‘c’ we get Table 5
Table 5
In table 5 the following 2 rules are in consistent
that means attribute ‘c’ is indispensable.
After removing attribute ‘d’ we get Table 6
Table 6
In table 6, the following rules make it inconsistent
therefore attribute ‘d’ is indispensable
Thus, (a,c,d) is the D-core and also the D-reduct
of C.
Therefore, we remove only attribute ‘b’, after which we also remove
redundancy that occurred because of the removal.
Table 7
• As there are similar decisions for different
conditions, we can group similar decisions into
decision classes.
(e2,f4) denoted as I
(e1,f4) denoted as II
(e2,f3) denoted as III
(e2,f2) denoted as IV
Table 8
Now we compute which attribute values are dispensable and
which ones are indispensable with respect to each decision class.
Values ‘a’ and ‘d’ are indispensable due to the following set of rules.
Core Values
Value Reduct
In the decision classes I and II sets of core
values of each decision rule are also
reducts
but the same does not apply for classes III
and IV.
Value Reducts
Table 10
References
• Chapter 9 Data Analysis
• Chapter 8 Slides – Gayatri and Bhargav
Thank You
Q&A