Chapter 1

Contents ,[object Object],[object Object],[object Object],[object Object],[object Object]

1.Introduction ,[object Object],[object Object]

[object Object],[object Object]

2.Knowledge and Classification ,[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

Table 1: Walk: An example decision table 26-49 46-60 x7 26-49 16-30 x6 26-49 46-60 x5 1-25 31-45 x4 1-25 31-45 x3 0 16-30 x2 50 16-30 x1 LEMS Age no yes no yes no no yes Walk

3.Knowledge Base ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Figure 2: Universe of Discourse U

Classification 1 Classification 2 Figure 3 C1 C5 C7 C8 C9 C2 C3 C4 C6 C1 C4 C3 C2 C1  C2 = 

[object Object],[object Object],[object Object],[object Object],Equivalence Relation is classification, So we will use R

More definitions: ,[object Object],[object Object],[object Object]

Indiscernibility relation ,[object Object],[object Object],[object Object],[object Object]

For more Clarification Example 3: X2 X1 X6 X5 X3 X4 U/R1={{X1},{X2,X3,X4},{X5,X6}} U/R2={{X1,X3,X4,X6},{X2,X5}} U/R3={{X1,X3,X4,X5,X6},{X2}} X1 X2 X4 X5 X6 X3 X1 X2 X3 X5 X6 X4

[object Object],[object Object],U/IND(P)={{X1},{X2},{X3,X4},{X5},{X6}} [ x ] IND (P) =  [x] R . R  P X1 X2 X4 X5 X6 X3

Clarifying Example 4 ,[object Object],[object Object],[object Object],[object Object],[x2] R1  [x2] R2 ={{X2,X3,X4}  {X2,X5}} = {X2} [x 2 ] IND(P) =  [x 2 ] R

Definitions: ,[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

Example5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

4.Equivalence of Knowledge ,[object Object],[object Object],[object Object],K ≃ K’ ,if IND (P) = IND (Q)

4.Generalization and Specialization of Knowledge ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],if P is finer than Q, then P is specialization of Q, and Q is generalization of P.

Example 6: U/Q U/P X1 X2 X4 X5 X6 X3 X1 X2 X4 X5 X6 X3 Q  P Q is finer than P P is coarser than Q

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