Finding Family Groups by Fuzzy Composition
Suppose in a matrix there are numbers indicating cross relations of families. It is willing to group the similar families using relation information. To solve this problem Fuzzy Composition can be used.
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.
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
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1, 1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
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
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
1, 1, 1,
1, 1, 1, 1, 1,
1, 1, 1,
1, 1, 1,
1, 1
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
1, 0, 0,
1, 0, 1, 0, 1,
1, 1, 0,
1, 1, 0,
1, 1
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
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
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
1, 0, 0,
1, 0, 1, 0, 1,
1, 1, 0,
1, 1, 0,
1, 1
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
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
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
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
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