U  x1
, x2
,..., x8 A = {F1, F2, F3, F4} = {Diploma, Experience, French, Reference} d = Decision Range set that belongs to properties: F1 = {1; 2; 3}; 1 = MBA, 2 = MCE, 3 = MSC F2 = {1, 2, 3}; 1 = Low, 2 = Medium, 3 = High F3 = {1, 2}; 1= Yes, 2 = No F4 = {1, 2, 3}; 1 = Neutral, 2 = Good, 3 = Excellent d = {0, 1}; 0 = Reject, 1 = Accept

## 2.2 Indiscernibility

A decision table clarifies all information about information system. This table may be very large. Same or indiscernible objects may be shown more than one or some properties may be redundant. 

If S = (*U, A*) is an information system for any BA, each subset of B properties defines an equivalence relation in U universe. The name of this relation is indiscernibility relation. For different two objects in U universe, the equivalence relation INDS(B) defined in below is called Bindiscernibility relation.

INDS(B)={(x,y)2 U│aB a(x)=a*(y)}* 
In indiscernebility relation S index is omitted when it is clear that which information system is referred. If (x,y)INDA(B), then x and y objects are indiscernible according to *B. x* and y objects are indiscernible because both of them have the same feature values and the decision can not be estimated. Before finding rule reducts in a decision table, it should be searched whether it has any indiscernible relations. Let Table 2.3 is handled after analyzing an information system. At first Table 2.3 is checked for indiscernible relations. It can be seen the objects 1 3 x , xand 4 5 x , xare indiscernible between each other. The reorganized decision table is shown in Table 2.4 below. Table 2.3: A Sample Decision Table Object F1 F2 F3 F4 **Decision**

1

x1 2 1 3 1

2

x1 1 1 1 0

3

x1 2 1 3 1

4

x3 3 1 1 1

5

x3 3 1 1 1

## 2.3 Rule Reduct Generation

One main concept in Rough Set Theory is rule reduct generation (RG). When there are a great variety of properties of objects, it is time consuming to control all properties. Especially when number of objects is high, solving the decision mechanism becomes very difficult. For 

| Table 2.4: The Reorganized Decision Table that has no indiscernible relation Object F1 F2 F3 F4   | Decision   |     |    |    |    |    |    |
|---------------------------------------------------------------------------------------------------|------------|-----|----|----|----|----|----|
| x                                                                                                 | 1          | 2   | 1  | 3  | 1  |    |    |
| x ,                                                                                               | 3          |     |    |    |    |    |    |
| 1 x                                                                                               | 1          | 1   | 1  | 1  | 0  |    |    |
| 2                                                                                                 |            |     |    |    |    |    |    |
| x                                                                                                 | ,          | 5 x | 3  | 3  | 1  | 1  | 1  |
| 4                                                                                                 |            |     |    |    |    |    |    |
