Find the Lower Approximation

Find Fuzzy Positive Region

Find Dependency Function

3.Dependency Function

Decision attribute contains two equivalence classes

U/Q = {{1,3,6}{2,4,5}}

With those elements belonging to the class possessing a

membership of one, otherwise zero

Normalize the given Dataset (conditional attribute)

Using Normalized table, Calculate the values of

N and Z.

N = All Negative values change to Zero,

Z = 1- ( Absolute Value of Normalized Table),

Equivalence classes are

U/A = {Na , Za}

U/B = {Nb , Zb}

U/C = {Nc , Zc}

U/Q = {{1,3,6},{2,4,5}}

Here, F= Na, Za, Nb, Zb, Nc, Zc

Inf - minimumSup - maximum

min (0.8, inf {1,0.2,1,1,1,1}) = 0.2

min (0.8, inf {1,0.2,1,1,1,1}) = 0.2

min (0.6, inf {1,0.2,1,1,1,1}) = 0.2

min (0.2, inf {1,0.2,1,1,1,1}) = 0

min (0.2, inf {1,0.2,1,1,1,1}) = 0

min (0.2, inf {1,0.2,1,1,1,1}) = 0

max (0.8,1.0) = 1.0

max (0.8,0.0) = 0.8

max (0.6,1.0) = 1.0

max (0.6,0.0) = 0.6

max (0.4,0.0) = 0.4

max (0.4,1.0) = 1.0

min(0.2,inf {1,0.8,1,0.6,0.4,1}) = 0.2

min(0.2,inf {1,0.8,1,0.6,0.4,1}) = 0.2

min(0.4,inf {1,0.8,1,0.6,0.4,1}) = 0.4

min(0.4,inf {1,0.8,1,0.6,0.4,1}) = 0.4

min(0.6,inf {1,0.8,1,0.6,0.4,1}) = 0.4

min(0.6,inf {1,0.8,1,0.6,0.4,1}) = 0.4

(maximum)

Here U/Q={{1,3,6}{2,4,5}}

(maximum)

= 2.0

Similarly we find

From this it can be seen that attribute B will cause the greatest increase in

dependency degree.

Here,

P = {A,B}

U/A = {Na,Za}

U/B = {Nb,Zb}

U/P= U/A U/B = {Na,Za} {Nb,Zb}

U/P = {Na ∩ Nb, Na ∩ Zb, Za ∩ Nb, Za ∩ Zb}

Similarly find Decision Table for,

U/{B,C} ={Nb ∩ Nc, Nb ∩ Zc, Zb ∩ Nc, Zb ∩ Zc},

U/{A,B,C}= {(Na ∩ Nb ∩ Nc), (Na ∩ Nb ∩ Zc), (Na ∩ Zb ∩ Nc),

(Na ∩ Zb ∩ Zc ), (Za ∩ Nb ∩ Nc), (Za ∩ Nb ∩ Zc),

(Za ∩ Zb ∩ Nc), (Za ∩ Zb ∩ Zc)}

Find Dependency Degree,

and,

As this causes no increase in dependency, the algorithm stops and outputs the reduct {A,B}.

The dataset can now be reduced to only those attributes appearing in the reduct.