fuzzy rough quickreduct algorithm
TRANSCRIPT
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.