Manual work for Fuzzy rough quickreduct algorithm

3.  Find the Lower Approximation
 Find Fuzzy Positive Region
 Find Dependency Function

5. 3.Dependency Function

7.  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)

9.  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}}

11. Here, F= Na, Za, Nb, Zb, Nc, Zc
Inf - minimum
Sup - maximum

13. 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

14. 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

15. 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

16. (maximum)

18. Here U/Q={{1,3,6}{2,4,5}}
(maximum)
= 2.0

19. Similarly we find
From this it can be seen that attribute B will cause the greatest increase in
dependency degree.

20. 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}

21. 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)}

22.  Find Dependency Degree,
and,

24.  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.