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Fuzzy rough quickreduct algorithm

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Dr.E.N.Sathishkumar

The document describes the steps to find a reduct using rough set theory which includes: 1. Finding the lower and positive approximations. 2. Calculating the dependency function which involves normalizing data and finding equivalence classes. 3. Iteratively adding attributes to determine which attribute combination causes the greatest increase in dependency degree to identify the optimal reduct.

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Fuzzy rough quickreduct algorithm
Fuzzy rough quickreduct algorithm
? Find the Lower Approximation ? Find Fuzzy Positive Region ? Find Dependency Function
Fuzzy rough quickreduct algorithm
3.Dependency Function
Fuzzy rough quickreduct algorithm
? 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)
Fuzzy rough quickreduct algorithm
? 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}}
Fuzzy rough quickreduct algorithm
Here, F= Na, Za, Nb, Zb, Nc, Zc Inf - minimum Sup - maximum
Fuzzy rough quickreduct algorithm
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)
Fuzzy rough quickreduct algorithm
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,
Fuzzy rough quickreduct algorithm
? 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.

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Fuzzy rough quickreduct algorithm

  • 3. ? Find the Lower Approximation ? Find Fuzzy Positive Region ? Find 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
  • 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.