Group Decision Making with AHP-OS

My AHP free online software AHP-OS has a feature to involve a group of decision makers to give their inputs to a decision problem. In contrast to my AHP Excel template, in AHP-OS the number of participants is practically unlimited. As of now, I see users having up to 100 participants in one project.

How to use AHP-OS for Group Decision Making?

As registered user you need to start with a new project by defining your decision hierarchy. In the Project Administration Menu click on New, define your hierarchy, Submit and Save as project. You have the possibility to give a short project description, explaining the project, before it is saved.

Once saved, you will be automatically brought back to your project page, and the project will be shown on top of your project list.


The session code is a unique code identifying the project. When you click on the session code link, the Group Session Input screen will open, and you see a message like “Hierarchy evaluation. Session code EvUhUn Session Chair: Klaus. Project has 0 participants’ inputs. You are participating as Klaus.” Now you can either participate yourself as a decision maker in the project, or get a link to provide to your participants for their inputs.

Participating by yourself as a member of the group

Simply click on the AHP button to start the pairwise comparisons, and – once completed – click on Submit for group eval to submit your inputs.

Provide a link to let others participate as members of the group

In the group input menu click on Leave group input mode and confirm ok to leave the input mode without submitting your pairwise comparisons in the pop-up window.


Now you will see the link that you can copy/paste and send to your group members for their participation in the project.


Click on Done in the Active session menu to go back to your project list.

Participants input

Your participants don’t need to be registered users. If you want to test by yourself, you need to logout from AHP-OS, before you open the group link.

When your participants open the link, they will be asked for their name, before they can start their pairwise comparisons. They will then see the decision hierarchy with a red lined AHP button and  a message “Click on AHP to complete pairwise comparisons. Click on Submit for group eval once completed.”


Now they can start their pairwise comparisons. When completed, all AHP buttons and priorities will be marked green.


After a click on Submit for group eval the AHP button disappears and a message “Ok. Data were submitted. Thank You for your participation!” is displayed.

Group results

Once you have participants submitted data, a click on the session code link in your project list will automatically bring you to the group result page. As a participant you will get a button View group result in the Group input menu.


The group result page gives you on top the project data and list of all participants. Individual participants can be selected or deselected to analyze the group results in further details.

projdata  partlist

The next sections of the group result page shows the decision hierarchy with consolidated priorities, a breakdown by nodes (categories) with priorities for the node and the consolidated (aggregated) decision matrix. It also shows the AHP consensus indicator as a measure of group consensus.


Input data for each participant is available under View Input Data in the group result menu:


For you as chair of the group session, it is also possible to download data as csv text file for further processing in a spreadsheet program. With Use consol. priorities you now can define Alternatives with the consolidated priorities of selected participants.



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AHP Online Software CSV Data Export

AHP-OS allows for downloading your project data as a comma separated value text file. The following menus include a csv download key:

  • Hierarchy Input Menu – download the AHP hierarchy
  • Group Result Menu – download resulting priorities and consolidated (aggregated) decision matrix
  • Project Data Menu – download decision matrices for all individual participants

Depending on your regional settings of your PC, for each download you can select the decimal point or decimal comma as decimal separator.

Text encoding of the CVS file is UTF-8. If you are using country specific characters and Windows Excel, you can convert from UTF-8 to ANSI. Open the CSV file with notepad, and save as a new file with Encoding set to ANSI.


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AHP Online Software – Decision Matrices – Update 2016-11-02

With the latest update of my AHP-OS online software you can now view and download the decision matrices of all participant. The group result menu was extended by a selection View Input Data:


From there you reach the Project Detailed Input page, which shows the decision matrix for each individual participant and all nodes of the hierarchy:


The project data menu has the button to download the data in csv format:


The csv file contains the basic project data – Session Code, Project Name, Project description, Author, Date, Type of evaluation, Number of Participants – as well as all input decision matrices sorted by participant and nodes (categories of the hierarchy) or criteria for alternative evaluation.

With the Back link you can go back to the Group Result Page.

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AHP Online Software – Latest Update 2016-10-29

Based on the request from some users I have modified the result display of my AHP-OS online software. Beside the resulting priorities it is now possible to see the underlying consolidated decision matrix, which results from the aggregation of individual judgments (AIJ) using the geometric mean.

Decision Hierarchies

For decision hierarchies the result page shows the resulting local and global priorities (overall result) in hierarchical form, and the global priorities in descending order in a bar graph.

Then, in a breakdown by nodes, consolidated priorities, consolidated decision matrix and the priorities of individual participants are shown:

As in this example, the consolidated matrix for one participant is the same as the AHP decision matrix.

Alternative Evaluation

For alternative evaluation the breakdown is done by criteria. It shows the consolidated preferences for all alternatives with respect to each of the criteria:


In this example the House A from the alternative houses A, B, C has the best match with respect to the criterion “Size”.


I am now working on the extension to let you download the complete set of input values, i.e. all underlying decision matrices, to excel. In the current version only the resulting AHP priorities are available.

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AHP Frequently Asked Questions

Over the year I receive many questions about AHP, my AHP excel template and my AHP online Software. Here a selection of frequently asked questions:

General Questions

Q: I have 15 criteria and 20 alternatives, can you extend your template/software?
A: The excel template can handle up to 10 criteria, my online software is limited to 12 criteria (in one hierarchy level) and 10 alternatives. In principle it could be extended, but the limitation is inherit to the AHP method. Please read my explanations here.

Q: I have more than 10 alternatives, can I use AHP for priority evaluation of criteria and a different method for the evaluation of alternatives?
A: Yes, you can combine AHP for criteria evaluation with another method for alternative evaluation. Alternative evaluation could be done for example using a simple table with a yes/no or applicable/not applicable scale, or any other scale, e.g. Likert scale, how good the individual alternative matches the specific criterion.

Q: I have 150 participants, can I use your excel template/software?
A: My AHP excel template is limited to 20 inputs, my AHP online software can handle a (practically) unlimited number of participants. Use the AHP online software.

Q: How can I resolve the inconsistency (CR>0.1), when participants are done with their pairwise comparisons.
A: Once the pairwise comparison is done and submitted, data can not be changed and consistency ratio is what it is. Ask your decision makers to adjust their judgments  in direction of the most consistent input during the pair-wise comparisons for the highlighted three most inconsistent comparisons. Please see also my posting here.

Q: Can I use the Likert scale instead of the AHP scale?
A: No, AHP is based on the rational scale 1/9 … 1 … 9. It cannot be replaced by the Likert scale.

Q: Do you support Fuzzy AHP?
A: No, I have made no provisions to support Fuzzy AHP, neither in Excel, nor in my online software.

Q: How is the computation done, where do I find the description and formulas?
A: Please download the manual for the excel template from here, and the software description from here.

Q: How can I cite your work, can you give me a reference?
A: Please cite my paper: Implementing the analytic hierarchy process as a standard method for multi-criteria decision making in corporate enterprises–a new AHP excel template with multiple inputs

AHP Excel template

Q: Can I extend the number of participants to more than 20?
A: Though it is possible in principle, the better way is to use my AHP online software with (practically) unlimited number of participants. I will not do a further extension of the template.

Q: Do you have a version of the Excel template w/o multiple inputs?
A: Yes, a simplified version is available on request from the author.

Q: How can I do alternative evaluation using your Excel template.
A: It is not possible. The template can only handle one category of a hierarchy and calculate the priority of one set of criteria.

AHP Online software

Q: If I have a group of decision makers, do they need to register for the online software?
A: No, they don’t need to register. As the owner of a project you get a link for group decision inputs. Simply send them the link, and they can start the pairwise comparisons.

Q: Can I erase/delete inputs from individual participants from the group results?
A: Sorry, at the moment there is no possibility to erase/delete inputs of individual participants. You can open a project with participants’ input and click “Use consol. priorities”. Then “Reset priorities” and “Save hierarchy”. Then you will have the same hierarchy as a new project without participants’ input.

Q: The alternative evaluation is not working?
A: Criteria evaluation (priorities) and alternative evaluation have to be handled as two different projects. Only when you have a decision hierarchy with completed comparisons and evaluated priorities, you can define the alternatives from the group result page clicking on “Use consol. priorities”. Define number and name of alternatives from there and save as new project. Hierarchy evaluation and alternative evaluation projects appear as type “H” for the first and type “A” for the latter in your project list.

Q: Can I get the source code of your online software?
A: Sorry, it is not an open source project.

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AHP Excel Template Version 2016-05-04

Just a small correction in the summary sheet: Now the correct name of the selected scale is displayed.

You can download the latest version of the AHP Excel Template from here.

Please consider a small donation, if you find the template useful for your work.

Incoming search terms:

  • AHP 20 latest correction
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Improving AHP consistency

In the implementation of both, AHP excel template as well as AHP online software, inconsistent judgments are highlighted and recommendations for consistent judgments are given.  How it is done, and what is the method behind?

The method is based on Saaty’s article “Decision-making with the AHP: Why is the principal eigenvector necessary“. European Journal of Operational Research 145 (2003) 85–91. He describes three methods how to transform a positive reciprocal matrix to a near consistent matrix.

In my implementation I construct the matrix εij = aij wj/wi to identify the three judgments for which εij is farthest from one. In Saaty’s paper it is shown as table 3, in my excel template it is called Consistency Error Matrix.  As I have to do it on each individual input sheet, I use as an approximation the RGMM (row geometric mean method) results, before calculating the eigenvector solution in the summary sheet.

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AHP online software – a reminder

If you are a registered user of my AHP online software, please keep in mind and be aware:

After 3 months of inactivity, your user account will be deactivated automatically. Please reactivate, using the link provided in the e-mail, if you want to keep your data, otherwise your account and all your data will be deleted 48 hours after deactivation.

This is done to ensure a slim database and help to keep the software fast and responsive. Please also avoid multiple registrations under different user names and e-mail addresses. You can keep up to 20 projects in your account, and it should be sufficient for the majority of users.

AHP online program limits:

  • Number of hierarchy levels: 6 max.
  • Number of hierarchy nodes: 50 max.
  • Number of criteria/node: 15 max. ( 7 to 9 recommended)
  • Number of hierarchy end nodes: 150 max.
  • Number of Alternatives: 10 max.
  • String length for nodes/leafs: 35 char max.
  • Number of characters for hierarchy definition: 6000

Thank you for your cooperation, and PLEASE – as a registered user – help to support this website with a small donation. I do not have a commercial interest, but I spend a lot of time, sharing my knowledge for free, and I have running costs to keep the site alive.

Thank you!

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AHP online software – how it was implemented

When I was asked just now in an e-mail, how my AHP online software operates,   I realized that I have never published a description about it. Therefore, here a short summary:

The AHP-OS software implementation is based on my AHP excel template. I have published one paper about it in 2013. All mathematical formulas used, are shown in this conference paper or in the excel template manual on the last 2 pages. The online version is realized in PHP, using OOP (object oriented programming), running on a Linux server.

The core module is the ahp class. It contains the routines to fill the decision matrix from the pairwise comparisons, to find the dominant eigenvalue using the power method, and to calculate the consistency ratio.

A second important class is the hierarchy class. It translates the text file – defining the hierarchy – into a hierarchical data array. When I implemented the software, I wanted to get a flexible tool, which can be used for all kind of hierarchical problems. This was actually more difficult than the implementation of all mathematical calculations, especially under the aspect of safety and malicious online attacks. The feature also differentiates the online version from the excel implementation. The excel template cannot handle hierarchies at all.

The third important class implements the database and its management. I use SQL with either sqlite or mysql drivers. There are 4 tables:

  • one for user management (registration, password, etc.),
  • one for projects (hierarchy data, description, session code etc.),
  • one for pairwise comparisons (participants, judgments etc.) and
  • one for handling alternatives.

The rest of classes contain supporting functions, like html in/output, excel download and consolidation for group results. I use a basically two open source packages, phpMailer and phpGraphlib, the rest is all realized by myself from scratch.

Please consider a donation, it will help me to maintain the website and program:

Your Donation (1 Singapore Dollar is approx. 0.7 USD):

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How to validate the correct software implementation of AHP?

Sometimes I receive the question, how to validate the correct implementation of my AHP excel template or my AHP online software, i.e. are the results correct and reliable? There are a number of steps to test the correct implementation of the method:

  1. Check for a 2 x 2 decision matrix.
  2. Use “1” for all elements of the decision matrix, i.e. each criterion has the same importance as all other criteria.
  3. Use extremes, i.e. one criterion is extremely (9 times) more important than all other criteria.
  4. Take specific examples from the literature – published research papers containing data of the decision matrix and priorities – and compare.
  5. Compare the results for same input data with the results from another software implementation of the AHP method.

This is what I have done, and in the following I will explain each step in more detail.

1. Check for a 2 x 2 decision matrix

For two criteria there is only one comparison and one solution only: If criterion A is x-times more important than B, the weight w(A) = x/(1+x). w(B) = 1-w(A) as w(A)+w(B) = 1. Eigenvalue = 2; CR is always 0.

Example: Criterion A is 3 times more important than criterion B:
w(A) = 3/4 (75%), w(B) = 1/4 (25%). Check: w(A)/w(B) = 3.

2. Each criterion has the same importance as all other criteria

If all criteria have the same importance, the resulting weight should be 1/n, with n the number of criteria.

Example: Four criteria should result in a weight of 1/4 = 25% for each criterion.

3. One criterion is 9 times more important than all other criteria

If one criterion is 9 times more important than all other criteria, the weights depend on the number of criteria, the maximum weight or maximum priority wmax is always

wmax = M/(n + M – 1)

with M = 9, the maximum of the AHP scale, and n the number of criteria. All other weights should be

wmin = (1 – wmax )/(– 1)

Example: 5 criteria, one criterion 9 times more important than all others

wmax = 9/(5 + 9 – 1) = 9/13 = 69.2%

wmin = (1 – 69.2% )/(5 – 1) = 0.31/4 = 7.7%

4. Specific examples from the literature

Here a practical example comparing the results with  an example (7 criteria) given by Saaty in Int. J. Services Sciences, Vol. 1, No. 1, 2008 (p 86, table 2). The AHP matrix is:

1 9 5 2 1 1  1/2
 1/9 1  1/3  1/9  1/9  1/9  1/9
 1/5 3 1  1/3  1/4  1/3  1/9
 1/2 9 3 1  1/2 1  1/3
1 9 4 2 1 2  1/2
1 9 3 1  1/2 1  1/3
2 9 9 3 2 3 1

The result according Saaty is
(0.177,  0.019, 0.042, 0.116, 0.190, 0.129, 0.327) with consistency ratio of 0,022

My AHP Excel template and my online software should give the same results.

5.  Comparison with other software implementations

As I have implemented AHP under Excel and written in php script language for the online version, I can simply compare the results from both implementations, using the same input data.

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