A revised version of my paper can now be downloaded:
Goepel, K.D., Comparison of Judgment Scales
of the Analytical Hierarchy Process - A New Approach, Preprint of an article submitted for consideration in International Journal of Information Technology and Decision Making © 2017 World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijitdm (2017)
Dear Friends, dear Visitors,
I wish all of you a Happy and Prosperous New Year 2018!
From July 13th to 15th the International Symposium on the Analytic Hierarchy Process (ISAHP) for Decision Making takes place in Hong Kong. Poster submission is possible from Nov 1st, 2017 to Mar 15th, 2018 and individual paper submission from Nov 1st, 2017 to Mar 6th. Early registration deadline May 15th, 2018. More Information about the ISAHP 2018 can be found on their website.
After my last participation in 2013, I plan to attend the conference in July. If you want to meet me personally, feel free to contact me. I submitted an individual paper about the implementation of my AHP-OS software; it is a short version of my detailed working paper. In additon I will probably submit a short version of my paper Comparison of Judgment Scales of the Analytical Hierarchy Process – A New Approach. This paper was submitted to the International Journal of Information Technology and Decision Making in June 2017, and is under review since then. All attempts to contact the editors and to find out, why the review process takes so long, were unsuccessful.
My AHP-OS software has now reached nearly 6000 registrations since its implementation in 2014. It should be quite stable and without major bugs. Unfortunately, there is still a minor sporadic problem with the storage of pairwise comparisons. It appears in 1 out of 1000 projects that a set pairwise comparisons just disappears. I am still trying to find the reason, kindly contact me, when this happens to you, and let me know the circumstances (It seems to have something to do with the browser and stored session data).
Please continue to support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.
For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.
Klaus D. Goepel,
Singapore, Jan 2018
BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.
The AHP consensus indicator, based on Shannon beta entropy (e.q. 1.1) for n criteria and k decision makers, was introduced in [1].
(1.1) Shannon beta entropy: 
(1.2) Shannon alpha entropy:
(1.3) Shannon gamma entropy: 
with 
The similarity measure S (eq. 1.4) depends on the number of criteria, and we used a linear transformation to map it to a range from 0 to 1 (eq. 1.5)
(1.4)
(1.5) Consensus (0% to 100%): 
In general Dα min = 1 and Dγ max = n. In the analytic hierarchy process (AHP) Dα min is a function of the maximum scale value M (M = 9 for the fundamental AHP scale) and the number of criteria n (eq. 1.6). The calculation of Dγ max was based on the assumption that respondents compare one distinct criterion M‑times more important than all others (eq. 1.7).
(1.6) 
(1.7)
This assumption is actually an unnecessary constrain, because even when the number of decision makers is less than the number of criteria, both can prioritize a complementing set of criteria as most important and as a result all consolidated criteria weights are equal. Therefore eq. 1.7 can be simplified to:
(1.8) 
As a result we get the AHP consensus indicator with:
(1.9) 
(1.10) AHP Consensus: 
Equation (1.10) is used in the latest updated of the AHP excel template and the AHP-OS online software.
[1] Klaus D. Goepel, (2013). 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, Proceedings of the International Symposium on the Analytic Hierarchy Process, Kuala Lumpur 2013
As I know from my own experience, manuals are seldomly read. On the other hand, a short guideline to complex software can be helpful, to use it effectively. I summarised the main menus of AHP-OS in a four page quick reference guide. The full manual is still available from the AHP-OS entry page (needs update …), and all details regarding methods and calculations are shown in my working paper about the AHP-OS software implemetation.
With the latest update of my AHP online software it is now possible to save judgments (pairwise comparisons) without completing the whole hierarchy evaluation. There are two scenarios, where this could be useful:
Pairwise comparison input is started as usually: either using the link provided on the project session page, or using the link AHP Group Session on the AHP-OS main entry page. After providong session code and name, in case the participant hasn’t given any input, a message Ok. Group has x participants. Click “Go” to continue will be displayed. Nodes without judgment show the AHP button with red outline.
Continue reading AHP-OS Hierarchy Evaluation with Partial Inputs from Participants
Dear Friends, dear Visitors,
Over the last three months I did a lot of under-the-hood changes and clean-up on the website to improve safety and user experience. As you may have noticed, the protocol is now https: the web traffic is encrypted using an SSL client certificate. After some tweaking the page performance could be improved significantly, loading time is nearly reduced by half. All pages, including my AHP-OS online software and the diversity calculator, were made mobile friendly, though I don’t recommend to use AHP-OS on a small mobile phone screen.
In addition some new features were added to the AHP-OS online software:
I also wrote a paper about the AHP software implementation, where you can find a description of the structure and all mathematical formulas and references. Please make a reference to this paper, when you use the software in your work to be published.
Kindly support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.
For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.
Klaus D. Goepel,
Singapore, September 2017
BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.
My online software AHP-OS is mainly used in research. Projects handled with AHP-OS cover a wide range of applications like healthcare, climate, risk assessment, supplier selection, hiring, IT, marketing, environment, transport, project management, manufacturing or quality assurance. Some of these projects could contain sensitive data. Therefore I finally decided to secure the site with HTTPS to protect the site and users.
The latest update of AHP-OS comprises of some minor changes to make the program flow easier to understand for participants w/o background in AHP.
For anyone, who is interested in the implementation of my free AHP-OS online software, and needs a reference:
Implementation of an online software for the Analytical Hierarchy Process
I hope to finalize the paper soon so that I can submit it for publication.
Sensitivity analysis is a fundamental concept in the effective use and implementation of quantitative decision models, whose purpose is to assess the stability of an optimal solution under changes in the parameters. (Dantzig)
In AHP the preference Pi of alternative Ai is calculated using the following formula (weighted sum model):
(1)
with Wj the weight of criterion Cj, and aij the performance measure of alternative Ai with respect to criterion Cj. Performance values are normalized.
(2)
Example
Sensitivity analysis will answer two questions:
changing the ranking between two alternatives?
