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Hi there!

I was wondering if anyone here could answer some questions of mine regarding the Analytic Hierarchy Process.

I am using AHP to determine the perceived importance of different factors based on the results of an online survey. I have 4 Criteria, with 4, 3, 3 and 2 sub-criteria respectively. I am using Excel for the analysis of the results.

I have created individual comparison matrices for each survey participant (or decision-maker) and normalized them. I used the arithmetic mean to get the perceived relative importance for each participant for all criteria and sub-criteria. By multiplying the relative importance of sub-criteria with the respective criteria of the higher level, I get the relative importance of all sub-criteria overall. I aggregate the individual priorities for the group with the geometric mean.

Since I am using Excel, I used an approximation of the principal eigen value to calculate the consistency index and ratio, based on the formula and random index suggested by Saaty. There are many cases, where the consistency ratio is varying degrees higher than the by Saaty recommended 10%.

I am not sure how to proceed to resolve these consistency issues.

Since the survey was conducted online with a large amount of participants, I can not contact participants to work out inconsistencies. Excluding participants which have a consistency ratio of more than 10% in any of the matrices due to inconsistency would drastically lower the amount of valid responses. In most cases, I am assuming that inconsistent values were given in error (whether it be due to lack of concentration, the complex topic of the survey or rank reversal phenomenon etc.).

There seem to be algorithms, which adjust the most inconsistent value with the expected one to increase consistency, but I am unable to implement such solutions (as I have no experience with R in this case) and am honestly out of my depth here.

Can small individual inconsistencies (if they are not so significant to be excluded entirely) be ignored, when the consistency of the aggregated group priority remains acceptable? I am not sure yet how to calculate the consistency of the aggregated group priority yet either.

Last but not least, I am going to attempt to calculate a group consensus indicator, but I haven't read up on that yet.

Any help, opinions or pointers what to read would be appreciated! I am getting a bit lost in reading about the AHP while being stuck on the consistency issue.

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