An Algorithm for Discretization of Real Value Attributes Based on Interval Similarity

Algorithm 1

Step1: Initialization. Set significance level 𝛼=0.5. Calculate inconsistency rate of information

   systems: Incon_rate.

Step2: Sort data in ascending order for each attribute and calculate 𝜒² value of

   each adjacent two intervals according to (1), then using a table to obtain

   the corresponding 𝜒² threshold. Calculate difference 𝐷^′=𝜒²_𝛼−𝜒²/√2𝑣.

Step3: Merge.

   While (mergeable cut point)

   {Search cut point that has the maximal difference 𝐷^′, then merging it;

    If Incon_rate change

     {Withdraw merging;

      goto Step4;}

    else goto Step2;

   }

Step4: If 𝛼 can not be decreased

       Exit procedure;

   Else {𝛼₀=𝛼;

      Decreasing the significance level by one level;

      goto Step2; }

Step5: Do until no attribute can be merged

   {For each mergeable attribute 𝑖

    {Calculate difference 𝐷^′;

     𝛼=𝛼₀;

     sign flag=0;

     While (flag= =0)

     {While (mergeable cut point)

        {Search cut point that has the maximal difference 𝐷^′, then merging it;

        If Incon_rate change

         {Withdraw merging;

         flag=1;

         break;}

         Else update difference 𝐷^′;

        }

      If 𝛼 can not be decreased

        Break;

      Else {Decreasing the significance level by one level;

       Update difference 𝐷^′;}

     }

    }

   }