On the mean random inconsistency index of analytic hierarchy process (AHP)

In this paper, we find a closed-form expression for the largest eigenvalue of a three-dimensional random pairwise comparison matrix. This expression can give us all the corresponding distribution moments. In particular, the exact value of the mean and variance of the largest eigenvalue associated a...

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Bibliographic Details
Published in:Computers & industrial engineering 1994-09, Vol.27 (1), p.401-404
Main Authors: Rao Tummala, V.M., Wan, Yat-wah
Format: Article
Language:English
Subjects:
Analytic Hierarchy Process
and Consistency ratio
Applied sciences
Decision theory. Utility theory
Eigenvalues
Exact sciences and technology
Hierarchies
Largest Eigenvalue Problem
Mathematical analysis
Mean Random Inconsistency Index
Operational research and scientific management
Operational research. Management science
Operations research
Simulation
Studies
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Summary:In this paper, we find a closed-form expression for the largest eigenvalue of a three-dimensional random pairwise comparison matrix. This expression can give us all the corresponding distribution moments. In particular, the exact value of the mean and variance of the largest eigenvalue associated a three-dimensional random pairwise comparison matrix are calculated, and are compared with those obtained by others on the topic. For n = 4 to 15, the mean and variance are determined by simulation. The number of simulation runs are determined by taking both the absolute and the relative simulation errors into the consideration.
ISSN:0360-8352
1879-0550
DOI:10.1016/0360-8352(94)90319-0