A note on the sampling distribution of the information content of the priority vector of a consistent pairwise comparison judgment matrix of AHP

V M Rao Tummala () and H Ling
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V M Rao Tummala: Eastern Michigan University
H Ling: Fudan University

Journal of the Operational Research Society, 2000, vol. 51, issue 2, 237-240

Abstract: Abstract The sampling distribution of the information content (entropy) of the priority vector of a consistent pairwise comparison judgment matrix, PCJM(n) using the Analytic Hierarchy Process (AHP) is studied by Noble and Sanchez, where n is the number of criteria associated with the matrix. They concluded simulation experiments with sample size of 1000 and found that the distribution is normal for n=4,5,...,15. When we increased the sample size to 2000, to 3000,..., to 8000, we found that the sampling distribution of entropy is not normal for all n, n=4,5,...,15. By using BestFit software system and using sample sizes of 8000, we found that the best-fitted and the second-best-fitted distributions of the entropy are either Weibull or normal for n⩾4. If we consider the most number of best fitted distributions as the criteria, then Weibull should be considered as the sampling distribution of the entropy for n⩾4. For n=3, beta should be considered as the best-fitted distribution.

Keywords: analytic hierarchy process; consistent matrix; priority vector; information content; entropy; sampling distribution of entropy (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1057/palgrave.jors.2600857

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