On Distribution Reduction and Algorithm Implementation in Inconsistent Ordered Information Systems

Algorithm 1

Input: An inconsistent ordered information system , where   and  .

Output: All distribution reductions of .

Step  1.  Load the ordered information system and simplify the system by combining the objects with same values of every

attribute,

Step  2.  Classify by every single criterion and store then in separate matrices

                .

                .

Step  3.  Check the consistence of the information system

        .

where “.*” is the operator in Matlab platform. If , the system is consistent, terminate the algorithm.

Else the system is inconsistent, go to the next step.

Step  4.  Acquire the consistent set. Let

        .

If , is a consistent set, store the set into the temporary storage cell. Else fetch another subset of and repeat this step.

Calculate till all subsets of are verified, then go to the next step.

Step  5.  Sort the consistent sets in the storage cell and find out the minimum consistent sets which are just the reductions.

Output all reductions and terminate the algorithm.