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CHAPTER 8 Decision Making CS267PowerPoint Presentation

CHAPTER 8 Decision Making CS267

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### Outline of the chapter

### Introduction

### Core and Reduct

### Simplification of decision table

### Check dependency of three of the following decision.conditionattribute decision attribute

### Reduction of condition attribute, if any. three of the following decision.

### Find core three of the following decision. values of all decision rules.

### Find three of the following decision.reducts of each decision rule.

### Combine and assign unique rule number to each rule. three of the following decision.

### Decision algorithm three of the following decision.

### Now combine the rules as per decision attribute, we will have decision algorithm

### Degree of dependency have decision algorithm

Introduction

Core and Reduct

Simplification of Decision Table

Decision Algorithm

Degree of Dependency

Definition:

For given KR system such that K = (U,A), we can define decision table 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

This decision table is also called ‘ CD – decision table’.

Core is a condition attribute value which is indispensable that means it discern 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.

It means removal of unnecessary conditions to make the

decision.

We will show it with the following steps listed.

Check dependency of conditionattribute decision attribute

Reduction of condition attribute, if any.

Find core values of all decision rules.

Find reducts of each decision rule.

Combine and assign unique rule number to each rule.

Let take the example of optician’s decision of whether the patient is suitable for contact lens or not.

We have set of condition a, b, c and d. which is shown below

a. Age

1. young

2. pre-presbyopic

3. prebyopic

b. Spectacle

1. myope condition

2. hypermetrope attributes

c. astigmatic

1. no

2. yes

d. tear production rate

1. reduced

2. normal

Based on given condition the optician has to take one out three of the following decision.

1. hard contact lens

2. soft contact lens decision attributes

3. no contact lens

So we have total of 24 (3*2*2*2) possible combination of given conditions which are shown with their decision in tabular form below.

Check dependency of three of the following decision.conditionattribute decision attribute

Reduction of condition attribute, if any.

Find core values of all decision rules.

Find reducts of each decision rule.

Combine and assign unique rule number to each rule.

every set of condition attribute must have unique decision attribute.

If the above shown condition is true for all decision rule then we say that dependency condition attribute decision attribute is valid.

Logically it is represented as below

{a,b,c,d} == > {e}

Check dependency of three of the following decision.conditionattribute decision attribute

Reduction of condition attribute, if any.

Find core values of all decision rules.

Find reducts of each decision rule.

Combine and assign unique rule number to each rule.

Now check for each condition attribute whether it is dispensable or indispensable with respect to decision attribute.

Suppose we are checking for condition attribute a in a given example.

Remove a and look for the rest of the condition attribute.(shown in figure)

After removal of a we have two pairs of decision rule which are inconsistent.

1. b2c2d2 e1 (rule 2)

b2c2d2 e3 (rule 18 and 24)

2. b1c1d2 e2 (rule 5)

b1c1d2 e3 (rule 20)

So condition attribute a is indispensable that means not removable.

Checking every condition attribute we found that every attribute is indispensable so no one is removable.

So now we can say that given table is e-independent.

After removal of condition attribute three of the following decision.a

Check dependency of three of the following decision.conditionattribute decision attribute

Reduction of condition attribute, if any.

Find core values of all decision rules.

Find reducts of each decision rule.

Combine and assign unique rule number to each rule.

We have to find out the core values of each decision rule in order to decide the reducts of that rule, because

core is an intersection of all reduct of same rule.

Consider the condition attribute and rules associated with decision attribute 1 that is e1.

If we want to find out the core of first rule that is a1b1c2d2 e1

First remove A and check for rest of attribute, you find that

b1c2d2 e1 (rule 1) and b1c2d2 e1 (rule 3)

which are inconsistent rule under decision attribute e1.

So attribute A of rule 1 is not core. Similarly B is also not core but C and D are core attribute for rule 1.

Check dependency of three of the following decision.conditionattribute decision attribute

Reduction of condition attribute, if any.

Find core values of all decision rules.

Find reducts of each decision rule.

Combine and assign unique rule number to each rule.

We have to add to the core value of each decision rule, such value of condition attribute of that rule so the

1. Predecessor of rule is independent.

2. The rule is true.

Suppose we are checking for first rule that is a1b1c2d2 e1

We already know that first rule has two core that is C and D. i.e.

U A B C D E

1 _ _ 2 2 1

So here we have three possibility of reduct which are

1 X 1 2 2 1 i.e. Rule b1c2d2 e1 possibility for

1 1 X 2 2 1 i.e. Rule a1c2d2 e1reducts of

1 X X 2 2 1 i.e. Rule c2d2 e1 first rule

Now check for every rule whether it is true or not.

Check dependency of three of the following decision.conditionattribute decision attribute

Reduction of condition attribute, if any.

Find core values of all decision rules.

Find reducts of each decision rule.

Combine and assign unique rule number to each rule.

In the last step we have to categorize the reducts which have the same decision rule.

And then assign a unique number to each of these decision rule, and it is your minimal decision table.

So after categorize the rules it will look like this three of the following decision.

And finally our minimal decision table will be as follows three of the following decision.

For making decision algorithm from decision table follow two steps.

1. replace all the value into the minimal decision table.

2. combine all the rules as per particular decision attribute.

From given minimal decision table we have the following rules.

a1c2d2 e1

b1c2d2 e1

a1c1d2 e2

a2c1d2 e2

b2c1d2 e2

d1 e3

a2b2c2 e3

a3b1c1 e3

a3b2c2 e3

By combining rules we have

(a1 V b1)c2d2 e1

(a1 V a2 V b2)c1d2 e2

d1 V (a3b2c1) V ((a2 V a3)b2c2) e3.

Which is our decision algorithm.

Degree of dependency can be calculated with the formulae

number of unaffected rule with lack of this attribute

degree of dependency = ----------------------------------------------------------------------

total number of rules

degree of dependency of a = 19 / 24 i.e. 5 rule affected (2,5,18,20,24)

degree of dependency of b = 3/4i.e. 6 rule affected

degree of dependency of c = 1/2i.e. 13 rule affected

degree of dependency of d = 1/4i.e. 18 rule affected

So attribute d is the most significant one in our decision table, because with the lack of attribute d, 18 rules are affected.

Q & A have decision algorithm

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