Cost-Sensitive Attribute Reduction in Decision-Theoretic Rough Set Models

Algorithm 2

An addition-deletion cost-sensitive attribute reduction algorithm.

Input: (𝑈,𝐶,𝐷,{𝑉_𝑎},{𝐼_𝑎},𝑡𝑐,(𝜆_𝑖𝑗)_2×3)

Output: The reduct 𝐴

Method:

(1) 𝐴=∅;

  //Addition

(2) 𝐶𝐴=𝐶;

(3) while  (𝑃𝑂𝑆_𝐴^(𝛼,𝛽)(𝐷)⊇𝑃̸𝑂𝑆_𝐶^(𝛼,𝛽)(𝐷)) do

(4) 𝑛=1; //𝑛 controls the dimension of 𝑆

(5) for  (each 𝑆⊆𝐶𝐴)  do

(6)  if   (|𝑆|=𝑛)  then

(7)   Compute 𝑓(𝐴,𝑆,𝑡𝑐);

(8)  end if

(9)  end for

(10) Select 𝑆^′ with the maximal 𝑓(𝐴,𝑆^′,𝑡𝑐);

(11)  if   (𝑓(𝐴,𝑆^′,𝑡𝑐)≤0)  then

(12)  𝑛++;

(13)  Go to line 5;

(14)  else

(15)  𝐴=𝐴∪𝑆^′; 𝐶𝐴=𝐶𝐴−𝑆^′;

(16)  end if

(17) end while

    //Deletion

(18) while  (ATC(𝑈,𝐴)>ATC(𝑈,𝐴−{𝑎}))  do

(19)  for  (each 𝑎∈𝐴)  do

(20)  Compute ATC(𝑈,𝐴−{𝑎});

(21)  end for

(22)  Select 𝑎^′ with the minimal ATC(𝑈,𝐴−{𝑎^′});

(23)  𝐴=𝐴−{𝑎^′};

(24) end while

(25) return 𝐴;