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

• Published in: Computers & industrial engineering Vol. 27; no. 1; pp. 401 - 404
• Main Authors: Rao Tummala, V.M., Wan, Yat-wah
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Seoul Elsevier Ltd 01.09.1994; Oxford Pergamon Press; New York, NY Pergamon Press Inc
• 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; and Consistency ratio; Largest Eigenvalue Problem; Analytic Hierarchy Process; Mean Random Inconsistency Index; Eigenvalue problem; Paired comparison; Decision theory; Analytic hierarchy process
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/0360-8352(94)90319-0

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.