Webb, J. (2018). Estimating uncertainty attributable to inconsistent pairwisecomparisons in the analytic hierarchy process (AHP). Unpublished PhD Praxis, George Washington University, Washington, DC.
Added by: Klaus D. Goepel (06 Jun 2019 05:16:27 Asia/Singapore) Last edited by: Klaus D. Goepel (08 Jun 2019 05:35:11 Asia/Singapore)
|Resource type: Thesis/Dissertation
BibTeX citation key: Webb2018
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|Categories: AHP/ANP, Decision Making
Keywords: Analytic Hierarchy Process (AHP), eigenvector method (EVM), geometric mean method, Monte-Carlo, uncertainty
Publisher: George Washington University (Washington, DC)
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This praxis explores a new approach to the problem of estimating the uncertainty attributable to inconsistent pairwise comparison judgments in the Analytic Hierarchy Process (AHP), a prominent decision-making methodology used in numerous fields, including systems engineering and engineering management. Based on insights from measurement theory and established error propagation equations, the work develops techniques to estimate the uncertainty of aggregated priorities for decision alternatives based on measures of inconsistency for component pairwise comparison matrices. This research develops two formulations for estimating the error: the first, more computationally intensive and accurate, uses detailed calculations of parameter errors to estimate the aggregated uncertainty, while the second, significantly simpler, uses an estimate of mean relative error (MRE) for each pairwise comparison matrix to estimate the aggregated error. This paper describes the derivation of both formulations for the linear weighted sum method of priority aggregation in AHP and uses Monte Carlo simulation to test their estimation accuracies for diverse problem structures and parameter values. The work focuses on the two most commonly used methods of deriving priority weights in AHP: the eigenvector method (EVM) and the geometric mean method (GMM). However, the approach of estimating the propagation of measurement errors can be readily applied to other hierarchical decision support methodologies that use pairwise comparison matrices. The developed techniques provide analysts the ability to easily assess decision model uncertainties attributable to comparative judgment inconsistencies without recourse to more complex optimization routines or simulation experiments described previously in the professional literature.