Simulation Experiments for Improving the Consistency Ratio of Reciprocal Matrices
Abstract
The consistency issue is one of the hot research topics in the analytichierarchy process (AHP) and analytic network process (ANP). To identify the mostinconsistent elements for improving the consistency ratio of a reciprocal pairwisecomparison matrix (PCM), a bias matrix can be induced to efficiently identify themost inconsistent elements, which is only based on the original PCM. The goal of thispaper is to conduct simulation experiments by randomly generating millions numbersof reciprocal matrices with different orders in order to validate the effectiveness ofthe induced bias matrix model. The experimental results show that the consistencyratios of most of the random inconsistent matrices can be improved by the inducedbias matrix model, few random inconsistent matrices with high orders failed theconsistency adjustment.References
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http://dx.doi.org/10.1037/h0070288
[2] Saaty, T. L. 1986. Axiomatic Foundation of the Analytic Hierarchy Process, Management Science 32(7): 841-855.
http://dx.doi.org/10.1287/mnsc.32.7.841
[3] Saaty, T. L. (1994), How to Make a Decision: The Analytic Hierarchy Process, Interfaces, 24: 19-43.
http://dx.doi.org/10.1287/inte.24.6.19
[4] Siraj, S.; Mikhailov, L.; Keane, J. (2012), A heuristic method to rectify intransitive judgments in pairwise comparison matrices, European Journal of Operational Research, 216: 420-428.
http://dx.doi.org/10.1016/j.ejor.2011.07.034
[5] Kou, G., Ergu,D., Shang,J. (2014). Enhancing Data Consistency in Decision Matrix: Adapting Hadamard Model to Mitigate Judgment Contradiction, European Journal of Operational Research, 236(1):261-271.
http://dx.doi.org/10.1016/j.ejor.2013.11.035
[6] Saaty, T. L. (1980), The Analytical Hierarchy Process, New York: McGraw-Hill.
[7] Saaty, T. L. (2003). Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research, 145(1): 85-91.
http://dx.doi.org/10.1016/S0377-2217(02)00227-8
[8] Ergu, D.; Kou, G.; Peng, Y.; Shi, Y. (2011). A Simple Method to Improve the Consistency Ratio of the Pair-wise Comparison Matrix in ANP, European Journal of Operational Research, 213(1): 246-259.
http://dx.doi.org/10.1016/j.ejor.2011.03.014
[9] Harker, P. T. 1987. Derivatives of the Perron root of a positive reciprocal matrix: With applications to the analytic hierarchy process, Applied Mathematics and Computation, 22: 217-232.
http://dx.doi.org/10.1016/0096-3003(87)90043-9
[10] Xu, Z., Wei, C. (1999),A consistency improving method in the analytic hierarchy process, European Journal of Operational Research, 116: 443-449.
http://dx.doi.org/10.1016/S0377-2217(98)00109-X
[11] Cao, D., Leung, L. C., Law, J. S. (2008). Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach, Decision Support Systems, 44: 944-953.
http://dx.doi.org/10.1016/j.dss.2007.11.002
[12] Choo, E., Wedley, W. (2004). A common framework for deriving preference values from pairwise comparison matrices, Computer and Operations Research, 31 (6): 893-908.
http://dx.doi.org/10.1016/S0305-0548(03)00042-X
[13] Lin, C. (2007). A revised framework for deriving preference values from pairwise comparison matrices, European Journal of Operational Research, 176 (2): 1145-1150.
http://dx.doi.org/10.1016/j.ejor.2005.09.022
[14] Kou,G, Lin,C. (2014). A cosine maximization method for the priority vector derivation in AHP, European Journal of Operational Research, 235:225-232.
http://dx.doi.org/10.1016/j.ejor.2013.10.019
Published
2014-06-15
How to Cite
ERGU, Daji et al.
Simulation Experiments for Improving the Consistency Ratio of Reciprocal Matrices.
INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 9, n. 4, p. 408-418, june 2014.
ISSN 1841-9844.
Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/1165>. Date accessed: 06 mar. 2021.
doi: https://doi.org/10.15837/ijccc.2014.4.1165.
Section
Articles
Keywords
Reciprocal random matrix, Consistency ratio, induced bias matrix, simulation experiment; analytic hierarchy process (AHP)/analytic network process (ANP)
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