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By studying AHP (Analytic Hierarchy Process), I have a question about RI. The (CI) is the consistency index. The RI value is fixed and is based on the number of criteria evaluated.

$CR = CI / RI$

My question is how did these values ​​RI? has a formula to calculate?

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RI stands for random index and represents an average CI for a huge number of randomly generated matrices of the same order. One can view it as an expected RI, so CR is the ratio between your consistency index and the expected one. The bigger it is, the worse your data is, by that measure. However, one should keep in mind that there is no definite measure of the "quality" of data in the decision theory.

You usually don't compute RI yourself, but use tables for that.

The concept of consistency, along with the consistency index, the random index, and the consistency ratio, was proposed by Saaty. He has done some initial computations as well, but since than I think statisticians have picked up and made more reliable tables.

More on the random index can be found in Donegan, Dodd, "A note on Saaty's random indexes".

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