Algorithm 1

Input: A neighborhood decision system NDS = (U, C, D, δ)

Output: A reduction attribute subset R

1. Initialize R = ∅.

2. while Sig(S, R, D) = 0 do

3.     Let Agent = R, and h = 0.

4.   for any a$\in$(S − R) do

5.      Compute Hδ(D, R$\cup${a}).

6.      if Hδ(D, R$\cup${a}) > h then

7.       Let Agent = R$\cup${a}, and h = Hδ(D, B$\cup${a}).

8.      end if

9.     end for

10.    Let R = Agent.

11. end while

12. Let r = |R|.

13. for i = 1 to r do

14.   Select ai$\in$R.

15.   Calculate Hδ(D, R − {ai}).

16.   if Hδ(D, R − {ai}) ≥ Hδ(D, C) then

17.    Let R = R − {ai}.

18. end

19. Return a reduction attributes subset R.