HDS :: AHP Calculations Background

CREATING THE AHP COMPARISON MATRIX

The following table shows the values and their description used for the comparison of relevant values of the elements of a typical AHP model.

Intensity of Importance	Definition	Explanation
1	Equal importance	Two activities contribute equally to the objective
3	Moderate importance	Experience and judgment slightly favor one activity over another
5	Strong importance	Experience and judgment strongly favor one activity over another
7	Very strong or demonstrated importance	An activity is favorad very strongly over another; its dominance demonstrated in practice
9	Extreme importance	The evidence favoring one activity over another is of the highest possible order of affirmation
2,4,6,8	Intermediate values

Let's examine the AHP scoring process and matrix creation in more detail.

With 3 treatment options to be compared (RxA, RxB, RxC), we can make subjective comparison judgments on which option we like best, as with the following:

RxA

RxB

RxA

RxC

RxB

RxC

Thus we have rated RxB better than RxA, RxA better than RxC, and RxB better than RxC. When we put these scores in the matrix, the diagonal is always 1. We fill in the top triangle of the matrix as shown below on the left matrix, Figure 1. To complete the full matrix we use the reciprocal values of the upper diagonal. The full, completed matrix is seen on the right side below, Figure 2.

Figure 1. Half of the matrix based on paired comparisons

Figure 2. Full matrix based on paired comparisons

To check if our opinions are consistent in our scoring, Saaty proposed what is called Consistency Ratio, which is a comparison between Consistency Index and Random Consistency Index (RI), or in formula:

CR = CI / RI
If the value of Consistency Ratio is smaller or equal to 10%, the inconsistency is acceptable. If the Consistency Ratio is greater than 10%, we need to consider revising our subjective judgments.

Random Consistency Index - RI - (for number of items compared in a matrix)
n	2	3	4	5	6	7	8	9	10
RI	0.00	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.51

References:

Teknomo, Kardi. Analytic Hierarchy Process Tutorial. Website - http://people.revoledu.com/kardi/tutorial/AHP

Saaty, T.J. How to make a decision: The analytic hierarchy process. European Journal of Operational Research, 1990, 48: 9-26.

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