With each attribute, we can associate an equivalence relation
Example:
“ Color ” attribute classifies all objects of the Universe into categories of objects having the same color, such as red, green, blue.
Each table can be viewed as a notion for a certain family of equivalence relations
5.
2.Examples Table 1 Objects in the information System are U1,…,U2. Attributes are Headache, Muscle pain, Temp, Flu
6.
[ Table 2 ] : Digits display unit in a calculator assumed to represent a characterization of “hand written” digits 1 1 0 1 1 1 1 9 1 1 1 1 1 1 1 8 0 0 0 0 1 1 1 7 1 1 1 1 1 0 1 6 1 1 0 1 1 0 1 5 1 1 0 0 1 1 0 4 1 0 0 1 1 1 1 3 1 0 1 1 0 1 1 2 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 G f e d c b a U a b c d e f g Objects in the information System are 1,…,9 Attributes are a, b, c, d, e, f, g
The value a(x) assigned by the primitive attribute a to the object x can be viewed as a name of primitive category of a to which x belongs (i.e. equivalence class of IND (a) containing x), that is to say a(x) is the name of [x] IND (a) .
Example:
If a(x)=2
That means that x
belongs to class 2
and will take its value
here if a(x)=2
x could be x 2, x3, x4,
each of them is on class 2 and take
Its value
Class 1 Class 2 Class 3 X1 X2 X4 X5 X6 X3
9.
Knowledge Representation System Vs Knowledge bases
There is a one-to-one correspondence between KRSs and KBs.
KRS S=( U,A ) may be viewed as a description of KB K= ( U, R)
KB
K=( U, R)
If , U/R ={X 1 ,…,X k }
KRS
S=( U,A )
The set of attributes A belongs every attribute a: U V aR ,such that V aR = {1,…,k} and a R (x)=i iff for i=1,…,k
Attribute in KRS = Equivalence relation Rows of a table = Name of categories
Compute whether all the attributes are of the same “ strength ” or not.
In order to find out the significance of a specific attribute it seems reasonable to drop the attribute from the table and see how the classification will be changed without this attribute.
If removing the attribute will change the classification it means that its significance is high – in the opposite case, the significance should be low .
As a measure of the significance of the subset of attributes with respect to the classification induced by a set of attributes C, we will mean the difference
∴ the attribute c is most significant, since it most changes the positive region of U/IND(D) significance of attribute ‘b’ : significance of attribute ‘c’ : significance of attribute ‘a’ :
All objects are explicitly represented and the attribute values, i.e., the table entries have associated explicit meaning as features or properties of the objects.
Actual dependencies existing in data, and data reduction, which is closer to statistical data model.
In Relational Model
It is not interested in the meaning of the information stored in the table.
Emphasis is placed on efficient data structuring and manipulation.
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