Chapter 9

Data AnalysisCS267

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 conditions1. 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 YouQ&A