AHP algorithm working only for 3 criteria

Question

I am trying to implement AHP(Analytic Hierarchy Process) algorithm for computing criterion's weights(using eigen vetors). For example, I want to buy a smart phone. My criteria are: color, memory, delivery. For computing weights I have to make pair wise comparison among criteria. I will compare color with memory, color with delivery, and memory with delivery. For comparing 2 criteria, we use a scale from 9 to 1/9. For example I compare color with memory: if in my opinion color is more important than memory 4 times, I will use 4 ,if color has the same importance like memory, I will use 1, if color is less important than memory 4 times, I use 1/4=0.25.
For computing weights, I have to build a matrix:

          color       memory       delivery

color     1           value1       value2

memory    1/value1      1          value3 

delivery  1/value2   1/value3       1

In my case the matrix is 3x3 because I have only 3 criteria. The program is working for 3 criteria, but not for 4, 5 or more. After the matrix is build, I can compute eigen vectors that will give me the weights.Any suggestion would be appreciated. Thank you in advance!

Here is the code for Criteria class:

public class Criteria
{
public static void main(String[] args)
{
    AHP ahp=new AHP();

    int n;
    int NUMBER_COMPARISON;
    Scanner keyboard=new Scanner(System.in);

    System.out.println("Enter the number of criteria");
    System.out.println("n=");
    n=keyboard.nextInt();
    NUMBER_COMPARISON=(n*n-n)/2;

    double [][] a=new double[n][n];
    String [] criteria=new String[n];
    double [] p=new double[NUMBER_COMPARISON];//used to hold the values of comparisons

    System.out.println("Enter the criteria:");
    for(int i=0; i<n;i++)
    {
        System.out.print("Criterion "+(i+1)+":");
        criteria[i]=keyboard.next();
    }

    System.out.println("Enter the comparison");
        int m=0; 
        for(int i=0; i<n;i++)
        {
            for(int j=i+1; j<n;j++)
            {
                System.out.println("Compare "+criteria[i]+" with "+criteria[j]+":");
                p[m]=keyboard.nextDouble();
                m++;
            }
        }

    a=ahp.initialize_matrix(p);
    ahp.show_matrix(a);
   }    
}

Here is the code for AHP class:

public class AHP
{
public static double[][] initialize_matrix(double[] p)
{
    //initialize the matrix a
    double a[][]=new double[p.length][p.length];    
    int k=0;        
    for(int i=0; i<p.length; i++)
    {
        for(int j=0; j<p.length;j++)
        {
            if(i==j)
                a[i][j]=1;
            else if(i<j)
            {

                a[i][j]=p[k];
                k++;
            }

            else if(i>j)
                a[i][j]=1/a[j][i];
        }
    }
    return a;
}

public static void show_matrix(double[][] b )
{
    //display the elements of the matrix a
    System.out.println("\nThe matrix a is:");
    for(int i=0; i<b.length;i++)
    {
        for(int j=0; j<b[i].length; j++)
            System.out.print(b[i][j]+"    ");
        System.out.println();   
    }
}
}

What exactly is the problem in case you have more than 3 criteria? Does the program throws an exception? — steffan, Oct 01 '12 at 17:52
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 6 at AHP.initialize_matrix(AHP.java:21) at Criteria.main(Criteria.java:61) — Lavinia, Oct 01 '12 at 17:59
For n criteria, the number of comparisons is equals (n*n-n)/2. For n=3 the number of comparisons is 3. I think this is why the program it is working for n=3. For n=4, for example, the number of comparisons is 6, and the program throws an exception. — Lavinia, Oct 01 '12 at 18:43
Thats the reason why you do not see the exception, because the array size is also 3 in this case. However, have a look at my update. — steffan, Oct 01 '12 at 19:17

steffan · Accepted Answer · 2012-10-01T19:15:05.973

From an analytical point of view the variables j and i in the initialize_matrix method are alway inside the array boundaries. However, there is the variable k, which can be incremented p.length^2 times. As you also use this variable to access the array p it must be < p.length.

I think you want to add the value at position k, but online every line. I suggest to set k to zero after the inner for loop is done.

EDIT: As predicted...

Output for n = 4:

Enter the number of criteria n= 4 Enter the criteria: Criterion 1:a Criterion 2:b Criterion 3:c Criterion 4:d Enter the comparison Compare a with b: 0.3 Compare a with c: 0.1 Compare a with d: 0.6 Compare b with c: 0.5 Compare b with d: 0.8 Compare c with d: 0.2

The matrix a is: 1.0 0.3 0.1 0.6 0.5 0.8
3.3333333333333335 1.0 0.3 0.1 0.6 0.5
10.0 3.3333333333333335 1.0 0.3 0.1 0.6
1.6666666666666667 10.0 3.3333333333333335 1.0 0.3 0.1
2.0 1.6666666666666667 10.0 3.3333333333333335 1.0 0.3
1.25 2.0 1.6666666666666667 10.0 3.3333333333333335 1.0

The method

public static double[][] initialize_matrix(double[] p)
{

    double a[][]=new double[p.length][p.length];    
    int k=0;        
    for(int i=0; i<p.length; i++)
    {
        k = 0;

        for(int j=0; j<p.length;j++)
        {
            if(i==j)
                a[i][j]=1;
            else if(i<j)
            {

                a[i][j]=p[k];
                k++;
            }

            else if(i>j)
                a[i][j]=1/a[j][i];
        }
    }
    return a;
}

I would appreciate it if you would mark the question as answered.

I follow your suggestion, for n=4, number of comparison 6. My matrix should be 3x3, but if I make the change, the program will show a matrix 6x6. So, I realized the correction should be in the method's header(AHP class): public static double[][] initialize_matrix(double[] p, int n), also double a[][]=new double[n][n]; for(int i=0; i — Lavinia, Oct 01 '12 at 20:26

AHP algorithm working only for 3 criteria

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