

 Making Comparison Matrix Read this tutorial comfortably offline, click here to purchase the ebook of this AHP tutorial. By now you know how to make paired comparisons. In this section you will learn how to make a reciprocal matrix from pair wise comparisons. For example John has 3 kinds of fruits to be compared and he made subjective judgment on which fruit he likes best, like the following
We can make a matrix from the 3 comparisons above. Because we have three comparisons, thus we have 3 by 3 matrix. The diagonal elements of the matrix are always 1 and we only need to fill up the upper triangular matrix. How to fill up the upper triangular matrix is using the following rules:
Comparing apple and banana, John slightly favor banana, thus we put in the row 1 column 2 of the matrix. Comparing Apple and Cherry, John strongly likes apple, thus we put actual judgment 5 on the first row, last column of the matrix. Comparing banana and cherry, banana is dominant. Thus we put his actual judgment on the second row, last column of the matrix. Then based on his preference values above, we have a reciprocal matrix like this To fill the lower triangular matrix, we use the reciprocal values of the upper diagonal. If is the element of row column of the matrix, then the lower diagonal is filled using this formula Thus now we have complete comparison matrix Notice that all the element in the comparison matrix are positive, or . Next section will discuss about how you will use this matrix. Click here to purchase the PDF copy of this AHP tutorial These tutorial is copyrighted. Do you have question regarding this AHP tutorial? Ask your question here Preferable reference for this tutorial is Teknomo, Kardi. (2006) Analytic Hierarchy Process (AHP) Tutorial . 



