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Normalisation and rank reversals in the additive analytic hierarchy process: a new analysis

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  • Sajjad Zahir

Abstract

We provide an explicit derivation of a new aggregation rule that naturally incorporates the relative strength of normalisation with respect to different criteria. The proposed aggregation procedure avoids unwanted rank reversals in the additive Analytic Hierarchy Process. In the case of absolute measure, the strength of normalisation is manifested by the priority vector's norm that can be interpreted as the unit of measure. However, when we have only relative judgements, norms are unknown and thus the decision maker has to estimate the relative strength of normalisation. Simultaneously, the new aggregation mechanism allows acceptable rank reversals if imperfections of human behaviour are recognised.

Suggested Citation

  • Sajjad Zahir, 2009. "Normalisation and rank reversals in the additive analytic hierarchy process: a new analysis," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 4(4), pages 446-467.
    • Handle: RePEc:ids:ijores:v:4:y:2009:i:4:p:446-467
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    Citations

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    Cited by:

    1. Weibing Sun & Fu Zhang & Shuya Tai & Jinkui Wu & Yaqiong Mu, 2021. "Study on Glacial Tourism Exploitation in the Dagu Glacier Scenic Spot Based on the AHP–ASEB Method," Sustainability, MDPI, vol. 13(5), pages 1-18, March.
    2. Vladimir Jakovljevic & Mališa Zizovic & Dragan Pamucar & Željko Stević & Miloljub Albijanic, 2021. "Evaluation of Human Resources in Transportation Companies Using Multi-Criteria Model for Ranking Alternatives by Defining Relations between Ideal and Anti-Ideal Alternative (RADERIA)," Mathematics, MDPI, vol. 9(9), pages 1-25, April.
    3. Liu, Xianliang & Liu, Yunfei, 2024. "Sensitivity analysis of the parameters for preference functions and rank reversal analysis in the PROMETHEE II method," Omega, Elsevier, vol. 128(C).
    4. Ardalan Bafahm & Minghe Sun, 2019. "Some Conflicting Results in the Analytic Hierarchy Process," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 465-486, March.
    5. Liu, Xianliang & Ma, Yonghao, 2021. "A method to analyze the rank reversal problem in the ELECTRE II method," Omega, Elsevier, vol. 102(C).
    6. Joanna Jaroszewicz & Anna Majewska, 2021. "Group Spatial Preferences of Residential Locations—Simplified Method Based on Crowdsourced Spatial Data and MCDA," Sustainability, MDPI, vol. 13(9), pages 1-24, April.

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