Chasan's Place - Finding Family Groups by Fuzzy Composition

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Fuzzy Composition

Finding Family Groups by Fuzzy Composition

A matrix contains numbers indicating cross relations of families. Is it possible to group the similar families? If yes, how can we use the relation information.

Solution lies on Fuzzy Composition.

Fuzzy Composition

P : Composition Relation

if then (a P c) = a () c.

To find Composition Relation, one technique is max-min composition. Here is the explanation of this technique:

C Source Code

This code is contains some bugs in finding number of families.

#include<stdio.h>

int A[16][16]={{10,  0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 0, 8, 0, 0, 6},
              {0, 10, 0, 0, 8, 0, 8, 2, 4, 0, 5, 0, 0, 8, 0, 0},
              {0,  0,10, 4, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 4, 0},
              {0,  0, 4,10, 0, 2, 0, 5, 8, 2, 2, 8, 4, 2, 8, 2},
              {0,  8, 0, 0,10, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 2},
              {5,  0, 2, 2, 0,10, 0, 8, 2, 0, 0, 0, 4, 0, 2, 8},
              {0,  8, 0, 0, 4, 0,10, 0, 4, 2, 8, 0, 0, 8, 0, 0},
              {4,  2, 2, 5, 0, 8, 0,10, 0, 0, 0, 0, 4, 0, 0, 4},
              {0,  4, 0, 8, 4, 2, 4, 0,10, 2, 4, 4, 0, 2, 2, 0},
              {0,  0, 2, 2, 0, 0, 2, 0, 2,10, 2, 8, 0, 2, 0, 0},
              {0,  5, 2, 2, 0, 0, 8, 0, 4, 2,10, 0, 0, 6, 0, 0},
              {0,  0, 2, 8, 0, 0, 0, 0, 4, 8, 0,10, 0, 0, 2, 0},
              {8,  0, 2, 4, 0, 4, 0, 4, 0, 0, 0, 0,10, 0, 8, 4},
              {0,  8, 0, 2, 4, 0, 8, 0, 2, 2, 6, 0, 0, 10,0, 2},
              {0,  0, 4, 8, 0, 2, 0, 0, 2, 0, 0, 2, 8, 0,10, 4},
              {6,  0, 0, 2, 2, 8, 0, 4, 0, 0, 0, 0, 4, 2, 4,10}};

int Numbers[5] = {2, 4 ,5, 6, 8};

int Maxx(int X[], int *imax)
{
   int i, min, max;
   max = 0;
   for(i=0;i<16;i++)
   {
               if ( X[i] > max)
                          max = X[i];
   }
   *imax = max;

   return 0;
}

int Find_R_Infinite()
{
   int B[16][16], R[16][16], imax, X[16];
   int i, j, t, k, z, son, ayni, tmp;

   for(i=0;i<16;i++)
   {
      for(j=0;j<16;j++)
      {
                 B[i][j] = A[i][j];
      }
   }

   son = 0;
   while (son == 0 )
   {
      for(i=0;i<16;i++)
      {
         for(k=0;k<16;k++)
         {
            t= 0;
            for(j=0;j<16;j++)
            {
               if ( A[i][j] < B[j][k])
                  z = A[i][j];
               else
                  z = B[j][k];
               X[t] = z;
               t++;
            }
            Maxx(X, &imax);
            R[i][k] = imax;
         }

      }

      ayni = 0;
      for(i=0;i<16;i++)
      {
         for(j=0;j<16;j++)
         {
            if (R[i][j] == A[i][j])
               ayni++;
         }
      }
      if (ayni == 16*16) // çik
                 son = 1;
      else
      {
         for(i=0;i<16;i++)
         {
            for(j=0;j<16;j++)
            {
               B[i][j] = A[i][j] = R[i][j];
            }
         }
      }
   }

   return 0;
}

int main(void)
{
   int i, j, k , m, n, Num[16][17], fam;
   FILE *f;

   Find_R_Infinite();

   f = fopen("r_infinite.txt", "w");
   for(i=0;i<16;i++)
   {
               for(j=0;j<16;j++)
               {
                          fprintf(f, "%3d, ", A[i][j]);
               }
               fprintf(f, "\n");
   }
   fclose(f);
   f = fopen("Families.txt","w");
   for(k=0;k<5;k++)
   {
      fam = 0;
      n = Numbers[k];
      fprintf(f, "For alpha=%d\n", n);
      for(i=0;i<16;i++)
      {
         for(j=0;j<16;j++)
         {
            if (A[i][j] >= n)
            {
                Num[i][j] = 1;
            }
            else
                Num[i][j] = 0;
            fprintf(f, "%2d, ", Num[i][j]);
         }
         fprintf(f, "\n");
      }

      fam = 0;
      for(i=0;i<16;i++)
      {
         j = 0;
         while ((j < i) && (Num[i][j] = 0))
            j++;
         if(j = i)
         {
            fam++;
         }
      }
      fprintf(f, "Number of families: %d, ", fam);
      fprintf(f, "\n\n");
    }

   return 0;
}

Sample Execution

Sample Matrix

10, 0, 0, 0, 0, 5, 0, 4, 0, 0, 0, 0, 8, 0, 0, 6

0, 10, 0, 0, 8, 0, 8, 2, 4, 0, 5, 0, 0, 8, 0, 0

0, 0, 10, 4, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 4, 0

0, 0, 4, 10, 0, 2, 0, 5, 8, 2, 2, 8, 4, 2, 8, 2

0, 8, 0, 0, 10, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 2

5, 0, 2, 2, 0, 10, 0, 8, 2, 0, 0, 0, 4, 0, 2, 8

0, 8, 0, 0, 4, 0, 10, 0, 4, 2, 8, 0, 0, 8, 0, 0

4, 2, 2, 5, 0, 8, 0, 10, 0, 0, 0, 0, 4, 0, 0, 4

0, 4, 0, 8, 4, 2, 4, 0, 10, 2, 4, 4, 0, 2, 2, 0

0, 0, 2, 2, 0, 0, 2, 0, 2, 10, 2, 8, 0, 2, 0, 0

0, 5, 2, 2, 0, 0, 8, 0, 4, 2, 10, 0, 0, 6, 0, 0

0, 0, 2, 8, 0, 0, 0, 0, 4, 8, 0, 10, 0, 0, 2, 0

8, 0, 2, 4, 0, 4, 0, 4, 0, 0, 0, 0, 10, 0, 8, 4

0, 8, 0, 2, 4, 0, 8, 0, 2, 2, 6, 0, 0, 10, 0, 2

0, 0, 4, 8, 0, 2, 0, 0, 2, 0, 0, 2, 8, 0, 10, 4

6, 0, 0, 2, 2, 8, 0, 4, 0, 0, 0, 0, 4, 2, 4, 10

Found Matrix

10, 4, 4, 8, 4, 6, 4, 6, 8, 8, 4, 8, 8, 4, 8, 6

4, 10, 4, 4, 8, 4, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4

4, 4, 10, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

8, 4, 4, 10, 4, 6, 4, 6, 8, 8, 4, 8, 8, 4, 8, 6

4, 8, 4, 4, 10, 4, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4

6, 4, 4, 6, 4, 10, 4, 8, 6, 6, 4, 6, 6, 4, 6, 8

4, 8, 4, 4, 8, 4, 10, 4, 4, 4, 8, 4, 4, 8, 4, 4

6, 4, 4, 6, 4, 8, 4, 10, 6, 6, 4, 6, 6, 4, 6, 8

8, 4, 4, 8, 4, 6, 4, 6, 10, 8, 4, 8, 8, 4, 8, 6

8, 4, 4, 8, 4, 6, 4, 6, 8, 10, 4, 8, 8, 4, 8, 6

4, 8, 4, 4, 8, 4, 8, 4, 4, 4, 10, 4, 4, 8, 4, 4

8, 4, 4, 8, 4, 6, 4, 6, 8, 8, 4, 10, 8, 4, 8, 6

8, 4, 4, 8, 4, 6, 4, 6, 8, 8, 4, 8, 10, 4, 8, 6

4, 8, 4, 4, 8, 4, 8, 4, 4, 4, 8, 4, 4, 10, 4, 4

8, 4, 4, 8, 4, 6, 4, 6, 8, 8, 4, 8, 8, 4, 10, 6

6, 4, 4, 6, 4, 8, 4, 8, 6, 6, 4, 6, 6, 4, 6, 10

Here are the family group matrices and numbers of families.

For alpha=2

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Number of families: 1

For alpha=4

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Number of families: 1

For alpha=5

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

Number of families: 3

For alpha=6

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1

Number of families: 3

For alpha=8

1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0

1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0

0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

Number of families: 4