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Dong, Y., Xu, Y., Li, H., & Dai, M. (2008). A comparative study of the numerical scales and the prioritization methods in AHP. European Journal of Operational Research, 186, 229–242. Added by: Klaus D. Goepel (07 Jun 2019 13:03:37 Asia/Singapore) Last edited by: Klaus-admin (11 Jun 2019 09:23:47 Asia/Singapore) |
| Resource type: Journal Article BibTeX citation key: Dong2008 Email resource to friend View all bibliographic details  |
Categories: AHP/ANP Keywords: comparison, eigenvector method (EVM), geometric mean method, logarithmic least squares method (LLSM), prioritization method, priority derivation, scale, scale functions Creators: Dai, Dong, Li, Xu Collection: European Journal of Operational Research |
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| Abstract |
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In the analytic hierarchy process (AHP), a decision maker first gives linguistic pairwise comparisons, then obtains numerical pairwise comparisons by selecting certain numerical scale to quantify them, and finally derives a priority vector from the numerical pairwise comparisons. In particular, the validity of this decision-making tool relies on the choice of numerical scale and the design of prioritization method. By introducing a set of concepts regarding the linguistic variables and linguistic pairwise comparison matrices (LPCMs), and by defining the deviation measures of LPCMs, we present two performance measure algorithms to evaluate the numerical scales and the prioritization methods. Using these performance measure algorithms, we compare the most common numerical scales (the Saaty scale, the geometrical scale, the Ma–Zheng scale and the Salo–Ha¨ma¨la¨inen scale) and the prioritization methods (the eigenvalue method and the logarithmic least squares method). In addition, we also discuss the parameter of the geometrical scale, develop a new prioritization method, and construct an optimization model to select the appropriate numerical scales for the AHP decision makers. The findings in this paper can help the AHP decision makers select suitable numerical scales and prioritization methods.
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