Dear Kardi, appreciate your tutorial and work put on-line, thank you! Was especially interested in AHP and learnt more about the method on your page. I have developed an excel sheet for it, which can be used for up to 8 elements - no makro. I also put a short video presentation on my youtube channel bpmsg. (http://www.youtube.com/bpmsg). I dont mind if you would put the excel template on-line, maube with a link to my channel. But please have a look at the template first. I\'ll send if you are interested and reply to my e-mail. Regards, Klaus

Hi Kardi-First of all, I appreciate your Web site on AHP. Great stuff. I am trying to use AHP for finding how groups of 5-10 people feel about certain topics. I am finding that the variety of responses sometimes leads to CR responses of greater than .10 - the threshold you suggest. For the groups, i have averaged the responses for each pairwise comparison. I have come across the GMM and WAMM methods for averaging responses for large groups with dissenting opinions. I haven\'t quite understood it yet, but that may be of assistance. Do you have any suggestions for dealing with high CR values?

Hi Eric, Saaty suggested a threshold of 10% for the CR values. In my opinion, the threshold of CR analogue to significant level of statistical analysis that related to confidence level of the analysis rather than a fixed value that everybody must follow. Having said that, if it is possible, the same respondents may also be asked again to reconsider their answers. You can use the CR as a feedback regarding their consistency.

Hello Mr. Teknomo, I guess you do not get messages like this one very often, but THANK YOU so much. I am writing my master\'s thesis and got to you page by chance looking for information about CR on AHP. I read by chance another page about alternative priorities and realized about a huge error on one of my thesis\' algorithms, which would have otherwise ruined and invalidated it. You explanation about composite priorities just saved my thesis. Kind regards, your contribution will be acknowledged. Jesus Calafat

Hi Jesus Calafat,Thank you for let me know that my work has been useful for you. Please visit my tutorials again next time and spread the words about these tutorials to your friends

We have a project approval committee conformed by 10 people. We want to use AHP for project ranking and I have made some web based questionnaire to be filled out by each decision maker. I am using a scale going for -9 up to +9 and for each pair wise comparison and I am averaging the 10 chosen numbers. Then I am introducing the gotten number in an AHP software. For the first test I got a CR = 11.2 %, which is close to 10%, the maximum allowed. Is this procedure OK? Thank you for your assistance. Carlos Barrios

Hi Carlos, AHP matrix must be positive matrix. Thus, you need to scale the negative value into 1 over that value. For group decision, many researchers recommended to use geometric mean rather than arithmetic mean for aggregation between actors. If you are not sure about the meaning of these averages, check my tutorial http://people.revoledu.com/kardi/tutorial/BasicMath/Average/index2.htm

Is it possible to obtain a negative consistency ratio in AHP? Many thanks in advance for your feedback! Best regards, Alina

Hi Alina, Negative CR is not possible and it may happen due to error in the approximation of eigen value. Remember that if you use MS Excel, it is only give you the approximation of eigen value, not the real one. Please use Matlab or mathematica. If you realy want to use Eigen value and Eigen vector for real problem using MS excel, I suggest you to install free Add Ins library matrix.xla from http://digilander.libero.it/foxes/SoftwareDownload.htm. It is a great program that you may use many matrix functions.

thqnks

Hello Sir, Pardon, for posted same question(@Alina). I still confuse and don\'t understand with Negative value on Consistency Ratio. I build a web based php+mysql dss with AHP model. I did a validate by input value based on a tutorial and result is match between tutorial and system But sometimes, once input custom value, the Consistency Ratio got negative on this system. Would you please share me advice how to handle this thank you very much Rajim Laymond

Excellent Tutorial on AHP. The lessions could have been posted also in provided in downloadable - pdf format. Any way thanks a lot.

my best regards to Mr Kardi Teknomo, that I\'ve learn much of his tutorials especially AHP

Hi Kardi, I want to know how to group the findings from a survey carried out using AHP. I want to know how people rate the importance of certain criteria Do I calculate the priority matrix for each survey response and do an average? Or is there any other method that can be used?

Usually we compute the priority matrix for each respondent first then make geometric average to aggregate the results. please check http://people.revoledu.com/kardi/tutorial/BasicMath/Average/geometric%20mean.html to learn about geometric mean

Thanks for the great tutorial!

thank u.

I think it would be of very much importance to have a SWOT analysis of the criterion first before we make our personal judgement on Criteria

First, thank you for your clear and excellent AHP tutorial. Second, I want to ask how to compute RI itself, for example: number of criteria is 20, then the formula to compute CR for matrik C (20X20) : CR = CI/RI. So how is the value of RI itself? Please help me with this problem.

As mentioned in the tutorial, the value of RI is provided by Prof. Saaty. It was generated using similar idea of Bootsrap using random reciprocal matrix of scale 1/9, 1/8, ... ,1, 2, .., 8, 9. In practice, you don't need RI for more than n=7 because the number of pair comparisons n*(n-1)/2 become so large. Too many questions on the same things make people confuse to answer them correctly.

Can you tell me the difference between AHP and DCE?