How to implement analytical hierarchy process (AHP)?

Dear Mojtaba

As far as I Know in AHP the Eigen Value method us used preferebly instead of the geometric mean. However, there is evidence that for a number alternatives greater than 3 it is more exact the geometric mean

Your second question is most important, and the same as I have been asking for years. Answers NONE.

AHP is based on the arbitrary estimates of the DM. But even, if there are reasoned estimates by using a group of DMs, comparing for instance, criterion 'Public health' and 'Environment' relative importance, I don't know how these two experts can agree. It is asumed that each one is an expert in his/her field, say expert A in public health and expert B in environment. They shear the characteristic that A can't evaluate the characteriscios of B, and vice versa, simply because they ignore each other field.

May be some AHP supporter can explain this.

Mojtaba Barzehkar

Thank you for your response. How the eigen value works? Could you please kindly explain?

Nolberto Munier

You can find the explanation on Eigen Value on any book or article on lineal algebra, even in wikipedia

The Eigen values are the roots of a characteristics polynomia defined by the initial matrix

The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to zero.

Fujun Hou

Hello, You may find the answer to [why geometric mean be used in analytical hierarchy process (AHP) instead of arithmetic mean, and how to check acceptable consistency on a pairwise comparison matrix] in the following paper:

Hou, F. (2018). On the hierarchical model PCbHA: a more general case. Soft Computing, 22(11), 3745-3756.

It is welcome to discuss anything about the model.

Fujun Hou

Hou, F. (2018). On the hierarchical model PCbHA: a more general case. Soft Computing, 22(11), 3745-3756.

Mojtaba Barzehkar

Thank you so much!

Sobur Setiaman

Implementing the Analytical Hierarchy Process (AHP) involves a series of steps to help make complex decisions by structuring problems, determining criteria, and comparing alternatives.

Here's a simplified step-by-step guide on how to implement AHP:

Define the Decision Problem: Clearly state the problem you want to solve and define the goal of your decision-making process. Identify the alternatives and criteria that will help you evaluate those alternatives.

Create a Hierarchy: Construct a decision hierarchy that consists of three levels: the goal, criteria, and alternatives. The top level is your primary goal, the middle level includes the criteria for evaluating alternatives, and the bottom level lists the available alternatives.

Assign Weights to Criteria: Determine the relative importance of each criterion with respect to the goal. Use a pairwise comparison method where you compare each criterion to every other criterion. You can use a scale (e.g., 1 to 9) to express the importance. These comparisons result in a matrix known as the Criteria Weight Matrix.

Calculate Criterion Weights: Normalize the Criteria Weight Matrix by calculating the weighted average for each criterion. This can be done using mathematical calculations to find the eigenvector associated with the matrix. This eigenvector provides the relative weights of each criterion.

Pairwise Comparison of Alternatives: Compare each pair of alternatives with respect to how well they satisfy each criterion. Assign scores based on their relative performance. Create a matrix known as the Alternatives' Performance Matrix.

Calculate Alternative Scores: Calculate the weighted sum for each alternative by multiplying the scores from the Alternatives' Performance Matrix by the weights of the corresponding criteria. This will give you an overall score for each alternative.

Check for Consistency: AHP includes a consistency check to ensure that your pairwise comparisons are reliable. You can use a consistency ratio to assess the consistency of your judgments. If the ratio is too high, you may need to review your comparisons and make adjustments.

Select the Best Alternative: The alternative with the highest overall score is considered the best choice according to AHP.

Sensitivity Analysis (Optional): Perform sensitivity analysis to see how sensitive your decision is to changes in the criteria weights or performance scores. This can help you understand the robustness of your decision.

Implement Your Decision: After selecting the best alternative, take action based on your decision.

Remember that AHP is a structured decision-making process that helps you make choices by quantifying and prioritizing criteria and alternatives.

It is essential to involve relevant stakeholders in the process and ensure that the pairwise comparisons accurately reflect their judgments.

There are also specialized software tools available that can streamline the calculations and make the AHP process more efficient.

Regenerate

Sobur Setiaman

https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/slides/saaty.pdf

Sobur Setiaman

Strategic Planning Software for Smarter Decisions http://www.expertchoice.com/2023

Mojtaba Barzehkar

Thank you

Nolberto Munier

Dear Sobur

What you say about that AHP is able to deal with complex decisions is inexact.

AHP uses a lineal top-down hierarchy that is no longer applicable to present-day complex problems where there are transversal, top-down and bottom-up decisions.

You say "Remember that AHP is a structured decision-making process that helps you make choices by quantifying and prioritizing criteria and alternatives"

Yes, by prioritizing criteria and alternatives with invented weights, according to a DM intuition.

Very scientific indeed!

You say "It is essential to involve relevant stakeholders in the process and ensure that the pairwise comparisons accurately reflect their judgments"

Mostly, stakeholders provide a lot of needed information, but they are not preapred to judge between criteria or alternatives, nor the DM

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