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

Algorithm 1

A backtracking algorithm to the MACR problem.

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

   current level test index lower bound 𝑙

Output: 𝑅 and cmc, they are global variables

Method: backtracking

   (1)  for (𝑖=𝑙;𝑖<|𝐶|;𝑖++) do

   (2)    𝐴=𝑅∪{𝑎_𝑖}

   (3)   if (𝑡𝑐(𝐴)≥cmc) then

   (4)    continue; //Pruning for too expensive test costs

   (5)   end if

   (6)  if  (ATC(𝑈,𝐴)<cmc)  then

   (7)     𝑐𝑚𝑐=ATC(𝑈,𝐴); //Update the minimal average total cost

   (8)     𝑅=𝐴; //Update the minimal total cost reduct

   (9)   end if

   (10) backtracking (𝐴,𝑖+1);

   (11) end for