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Influence of aggregation and measurement scale on ranking a compromise alternative in AHP


  • Alessio Ishizaka

    (University of Portsmouth, Portsmouth Business School)

  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Todd Kaplan

    (Department of Economics, University of Exeter)


Analytic Hierarchy Process (AHP) is one of the most popular multi-attribute decision aid methods. However, results depend on the preference measurement sacle and the aggregation technique used. In this paper, we describe a decision problem with an inherent trade-off between two criteria. A decision-maker has to choose among three alternatives: two extremes and one "compromise". Six different measurement scales described previously in the literature and the new proposed logarithmic scale are considered for applying the additive and the multiplicative AHP. The results are compared with the standard consumer choice theory. The geometric and power scales offer no chance (for the additive AHP) and very few chances (for the multiplicative AHP) for a compromise to be selected. The logarithmic scale used with the multiplicative AHP is the most in agreement with the consumer choice theory.

Suggested Citation

  • Alessio Ishizaka & Dieter Balkenborg & Todd Kaplan, 2005. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Discussion Papers 0506, University of Exeter, Department of Economics.
  • Handle: RePEc:exe:wpaper:0506

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    References listed on IDEAS

    1. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    2. Vargas, Luis G., 1990. "An overview of the analytic hierarchy process and its applications," European Journal of Operational Research, Elsevier, vol. 48(1), pages 2-8, September.
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    5. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 387-400, December.
    6. Lootsma, F. A., 1989. "Conflict resolution via pairwise comparison of concessions," European Journal of Operational Research, Elsevier, vol. 40(1), pages 109-116, May.
    7. Robert L. Winkler, 1990. "Decision Modeling and Rational Choice: AHP and Utility Theory," Management Science, INFORMS, vol. 36(3), pages 247-248, March.
    8. Patrick T. Harker & Luis G. Vargas, 1987. "The Theory of Ratio Scale Estimation: Saaty's Analytic Hierarchy Process," Management Science, INFORMS, vol. 33(11), pages 1383-1403, November.
    9. Stam, Antonie & Duarte Silva, A. Pedro, 2003. "On multiplicative priority rating methods for the AHP," European Journal of Operational Research, Elsevier, vol. 145(1), pages 92-108, February.
    10. Lootsma, F. A. & Mensch, T. C. A. & Vos, F. A., 1990. "Multi-criteria analysis and budget reallocation in long-term research planning," European Journal of Operational Research, Elsevier, vol. 47(3), pages 293-305, August.
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    Cited by:

    1. Alessio Ishizaka, 2014. "Comparison of fuzzy logic, AHP, FAHP and hybrid fuzzy AHP for new supplier selection and its performance analysis," International Journal of Integrated Supply Management, Inderscience Enterprises Ltd, vol. 9(1/2), pages 1-22.
    2. Jih-Jeng Huang & Masahiro Inuiguchi, 2015. "Diminishing Utility Decision Model for Weighting Criteria," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1263-1284, November.
    3. Jordi Gallego-Ayala & Dinis Juízo, 2014. "Integrating Stakeholders’ Preferences into Water Resources Management Planning in the Incomati River Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(2), pages 527-540, January.
    4. J. Hummel & John Bridges & Maarten IJzerman, 2014. "Group Decision Making with the Analytic Hierarchy Process in Benefit-Risk Assessment: A Tutorial," The Patient: Patient-Centered Outcomes Research, Springer;Johns Hopkins Bloomberg School of Public Health, vol. 7(2), pages 129-140, June.
    5. Dong, Yucheng & Hong, Wei-Chiang & Xu, Yinfeng & Yu, Shui, 2013. "Numerical scales generated individually for analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 229(3), pages 654-662.
    6. Siraj, Sajid & Mikhailov, Ludmil & Keane, John A., 2015. "Contribution of individual judgments toward inconsistency in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 242(2), pages 557-567.
    7. Ishizaka, Alessio & Balkenborg, Dieter & Kaplan, Todd R, 2010. "Does AHP help us make a choice? - An experimental evaluation," MPRA Paper 24213, University Library of Munich, Germany.
    8. Susanna Sironen & Jyri Seppälä & Pekka Leskinen, 2015. "Towards more non-compensatory sustainable society index," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 17(3), pages 587-621, June.
    9. Marion Danner & Vera Vennedey & Mickaël Hiligsmann & Sascha Fauser & Christian Gross & Stephanie Stock, 2016. "How Well Can Analytic Hierarchy Process be Used to Elicit Individual Preferences? Insights from a Survey in Patients Suffering from Age-Related Macular Degeneration," The Patient: Patient-Centered Outcomes Research, Springer;Johns Hopkins Bloomberg School of Public Health, vol. 9(5), pages 481-492, October.
    10. Siraj, S. & Mikhailov, L. & Keane, J.A., 2012. "Preference elicitation from inconsistent judgments using multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 220(2), pages 461-471.

    More about this item


    : Decision Analysis; Multiple criteria analysis; Utility theory; Additive AHP; Multiplicative AHP; Logarithmic scale;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General


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