Can anyone familiar with the Analytic Hierarchy Process (AHP) instrument discuss on the permissible limit of the Consistency Ratio (CR). Although T. L. Saaty allows a limit of not more than 0.1, there are authors who allow the CR untul 0.2. Will it be okay to use the 0.2 CR limit? Thank you.
It would be around 0.10 (Saaty 1990). But, more than the threshold value (approx 0.15) is also permissible with some special cases.
It depends on the matrix size. The greater the size of the matrix, the more CR values > 0.1 are acceptable. See, for example, WC Wedley 'Consistency Prediction for incomplete AHP matrices' (1993) for details.
Following paper may be referred that is available at researchgate:
Analytical Hierarchy Process Applied to Vendor Selection Problem: Small Scale, Medium Scale and Large Scale Industries
Kumar Sanjay, Parashar Neeraj, Dr. Abid Haleem
CR depends mainly on the matrix size following the recommendations of "WC Wedley, 1993 Consistency Prediction for incomplete AHP matrices". In addition, it depends on the sample characteristics and the analysis (group and/or individual), for individuals experts, CR is restricted to 0.10 or 0.15, while for group responds CR could be relaxed to 0.20 to allow for non-expert responds following the recommendations of "Ho, D., Newell, G. and Walker, A. (2005). The importance of property-specific attributes in assessing CBD office building quality. Journal of Property Investment & Finance, 23(5), 424-444".
Dear ALL. Thank you very much for your comments and recommending the relevant articles. They have been helpful in developing my understanding on the use of CR beyond 0.1 until 0.2. From my own experience from conducting interviews and surveys with maritime experts, it was not easy to persuade them to agree with a pairwise comparison that would come to a CR of 0.1 and below. For them, things are not as straight forward as a simple comparison such as when A is 3x better than B, and B is 3x better than C, than A should be 6x better than C. I also believe a CR of 0.2 would be more practicable in allowing for some flexibility for the respondents to express their judgments without the worry of getting their judgments rejected because of non-conformance with the 0.1 CR requirement. Thank you once again.
This is a good question.
Equally good is the normalizing mapping approach in handling piecewise comparisons (PCs) in solving the PC rating paradox in
W.W. Koczkodaj, Pairwise Comparisons Rating Scale Paradox, arXiv Dec 2015:
http://arxiv.org/pdf/1511.07540v2.pdf
See Section 3, starting on page 5 for the normalizing mapping as a means of solving the PC rating paradox.
Dear Waldemar,
It seems to me that you do not tell the whole truth about your text with the paradox. Let me recall to you that I have corrected several mistakes in the drafts of your text that you seem to be so proud of. I have also improved some pieces of mathematics.. You have mentioned about my contribution in your Acknowedgments. Thank you. I'm afraid that without my contribution your text would be rejected from publication. Of course, it is possible that other reseachers will extend some of your ideas in a not-too-distant future, especially some of the researchers who like to write a lot of articles may want to develop the ideas of your text and publish more. Some time ago, I also told you that not everything around scales had been done well enough. There is a mess even in definitions of scales and of scaling process. Of course, Waldemar, you have given me enough credits for the improvements of your paradox text and I do not want more credits for it. Of course, one can try to find better solutions to your paradox and better answers to the main question.
Regards, Eliza Wajch
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