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Numerical scales generated individually for analytic hierarchy process

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  • Dong, Yucheng
  • Hong, Wei-Chiang
  • Xu, Yinfeng
  • Yu, Shui

Abstract

Because individual interpretations of the analytic hierarchy process (AHP) linguistic scale vary for each user, this study proposes a novel framework that AHP decision makers can use to generate numerical scales individually, based on the 2-tuple linguistic modeling of AHP scale problems. By using the concept of transitive calibration, individual characteristics in understanding the AHP linguistic scale are first defined. An algorithm is then proposed for detecting the individual characteristics from the linguistic pairwise comparison data that is associated with each of the AHP individual decision makers. Finally, a nonlinear programming model is proposed to generate individual numerical scales that optimally match the obtained individual characteristics. Two well-known numerical examples are re-examined using the proposed framework to demonstrate its validity.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:3:p:654-662
    DOI: 10.1016/j.ejor.2013.03.019
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    1. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 700-710, April.
    2. Siraj, Sajid & Mikhailov, Ludmil & Keane, John, 2012. "A heuristic method to rectify intransitive judgments in pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 420-428.
    3. 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.
    4. P Ji & R Jiang, 2003. "Scale transitivity in the AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 896-905, August.
    5. Finan, J. S. & Hurley, W. J., 1999. "Transitive calibration of the AHP verbal scale," European Journal of Operational Research, Elsevier, vol. 112(2), pages 367-372, January.
    6. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi, 2008. "On consistency measures of linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 189(2), pages 430-444, September.
    7. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Does AHP help us make a choice? An experimental evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1801-1812, October.
    8. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Dai, Min, 2008. "A comparative study of the numerical scales and the prioritization methods in AHP," European Journal of Operational Research, Elsevier, vol. 186(1), pages 229-242, April.
    9. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
    10. Grošelj, Petra & Zadnik Stirn, Lidija, 2012. "Acceptable consistency of aggregated comparison matrices in analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 223(2), pages 417-420.
    11. Huizingh, Eelko K. R. E. & Vrolijk, Hans C. J., 1997. "A Comparison of Verbal and Numerical Judgments in the Analytic Hierarchy Process," Organizational Behavior and Human Decision Processes, Elsevier, vol. 70(3), pages 237-247, June.
    12. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Does AHP help us make a choice? An experimental evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1801-1812, October.
    13. 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.
    14. Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
    15. Ergu, Daji & Kou, Gang & Peng, Yi & Shi, Yong, 2011. "A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP," European Journal of Operational Research, Elsevier, vol. 213(1), pages 246-259, August.
    16. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    Cited by:

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    2. Bice Cavallo & Alessio Ishizaka, 2023. "Evaluating scales for pairwise comparisons," Annals of Operations Research, Springer, vol. 325(2), pages 951-965, June.
    3. Zhu, Bin & Xu, Zeshui, 2014. "Analytic hierarchy process-hesitant group decision making," European Journal of Operational Research, Elsevier, vol. 239(3), pages 794-801.
    4. Li, Cong-Cong & Dong, Yucheng & Liang, Haiming & Pedrycz, Witold & Herrera, Francisco, 2022. "Data-driven method to learning personalized individual semantics to support linguistic multi-attribute decision making," Omega, Elsevier, vol. 111(C).
    5. Xia, Meimei & Chen, Jian, 2015. "Multi-criteria group decision making based on bilateral agreements," European Journal of Operational Research, Elsevier, vol. 240(3), pages 756-764.
    6. Ho, William & Ma, Xin, 2018. "The state-of-the-art integrations and applications of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 267(2), pages 399-414.
    7. Yuji Sato & Kim Hua Tan, 2023. "Inconsistency indices in pairwise comparisons: an improvement of the Consistency Index," Annals of Operations Research, Springer, vol. 326(2), pages 809-830, July.
    8. Wu, Xingli & Liao, Huchang, 2019. "A consensus-based probabilistic linguistic gained and lost dominance score method," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1017-1027.

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