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Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices

Author

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  • Li, Kevin W.
  • Wang, Zhou-Jing
  • Tong, Xiayu

Abstract

Existing research on acceptability of pairwise interval comparison matrices focuses on acceptable consistency by controlling their inconsistency levels to within a certain threshold. However, a perfectly consistent but highly indeterminate interval comparison matrix can be unacceptable as it contains little (sometimes no) useful decision information. This paper first analyzes the current definition of acceptable consistency for interval multiplicative comparison matrices (IMCMs) and shows its technical deficiencies. We then introduce a new notion of acceptable IMCMs, considering both inconsistency and indeterminacy levels in IMCMs. A geometric-mean-based index is proposed to measure the indeterminacy ratio of an IMCM, and useful properties are derived for consistent IMCMs and acceptable IMCMs. An indeterminacy-ratio and geometric-mean-based transformation equation is subsequently put forward to convert normalized acceptable interval multiplicative weights into an acceptable IMCM with consistency. By introducing an auxiliary constraint, a logarithmic least square model is established to generate interval multiplicative weights from acceptable IMCMs. A geometric-mean-based possibility degree formula is designed to compare and rank normalized interval multiplicative weights. Two numerical examples are presented to illustrate how to utilize the proposed framework.

Suggested Citation

  • Li, Kevin W. & Wang, Zhou-Jing & Tong, Xiayu, 2016. "Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices," European Journal of Operational Research, Elsevier, vol. 250(2), pages 628-638.
  • Handle: RePEc:eee:ejores:v:250:y:2016:i:2:p:628-638
    DOI: 10.1016/j.ejor.2015.09.010
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    References listed on IDEAS

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    1. Aguaron, Juan & Moreno-Jimenez, Jose Maria, 2003. "The geometric consistency index: Approximated thresholds," European Journal of Operational Research, Elsevier, vol. 147(1), pages 137-145, May.
    2. Guo, Peijun & Tanaka, Hideo, 2010. "Decision making with interval probabilities," European Journal of Operational Research, Elsevier, vol. 203(2), pages 444-454, June.
    3. 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.
    4. Merigó, José M. & Casanovas, Montserrat & Yang, Jian-Bo, 2014. "Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators," European Journal of Operational Research, Elsevier, vol. 235(1), pages 215-224.
    5. Borgonovo, Emanuele & Marinacci, Massimo, 2015. "Decision analysis under ambiguity," European Journal of Operational Research, Elsevier, vol. 244(3), pages 823-836.
    6. Sugihara, Kazutomi & Ishii, Hiroaki & Tanaka, Hideo, 2004. "Interval priorities in AHP by interval regression analysis," European Journal of Operational Research, Elsevier, vol. 158(3), pages 745-754, November.
    7. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    8. Ahn, Byeong Seok & Park, Haechurl, 2014. "Establishing dominance between strategies with interval judgments of state probabilities," Omega, Elsevier, vol. 49(C), pages 53-59.
    9. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    10. Wang, Zhou-Jing & Li, Kevin W., 2015. "A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices," European Journal of Operational Research, Elsevier, vol. 242(3), pages 890-900.
    11. Rezaei, Jafar & Ortt, Roland, 2013. "Multi-criteria supplier segmentation using a fuzzy preference relations based AHP," European Journal of Operational Research, Elsevier, vol. 225(1), pages 75-84.
    12. Durbach, Ian & Lahdelma, Risto & Salminen, Pekka, 2014. "The analytic hierarchy process with stochastic judgements," European Journal of Operational Research, Elsevier, vol. 238(2), pages 552-559.
    13. Zhu, Bin & Xu, Zeshui, 2014. "Analytic hierarchy process-hesitant group decision making," European Journal of Operational Research, Elsevier, vol. 239(3), pages 794-801.
    14. Stein, William E. & Mizzi, Philip J., 2007. "The harmonic consistency index for the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 177(1), pages 488-497, February.
    15. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
    16. Wang, Ying-Ming & Elhag, Taha M.S., 2007. "A goal programming method for obtaining interval weights from an interval comparison matrix," European Journal of Operational Research, Elsevier, vol. 177(1), pages 458-471, February.
    17. Yan, Hong-Bin & Ma, Tieju, 2015. "A group decision-making approach to uncertain quality function deployment based on fuzzy preference relation and fuzzy majority," European Journal of Operational Research, Elsevier, vol. 241(3), pages 815-829.
    18. Entani, Tomoe & Sugihara, Kazutomi, 2012. "Uncertainty index based interval assignment by Interval AHP," European Journal of Operational Research, Elsevier, vol. 219(2), pages 379-385.
    19. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    20. 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.
    21. Scholten, Lisa & Schuwirth, Nele & Reichert, Peter & Lienert, Judit, 2015. "Tackling uncertainty in multi-criteria decision analysis – An application to water supply infrastructure planning," European Journal of Operational Research, Elsevier, vol. 242(1), pages 243-260.
    22. 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.
    23. Brunelli, Matteo & Fedrizzi, Michele, 2015. "Boundary properties of the inconsistency of pairwise comparisons in group decisions," European Journal of Operational Research, Elsevier, vol. 240(3), pages 765-773.
    24. Xu, Zeshui & Chen, Jian, 2008. "Some models for deriving the priority weights from interval fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 184(1), pages 266-280, January.
    25. Wang, Zhou-Jing, 2015. "A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”," European Journal of Operational Research, Elsevier, vol. 247(3), pages 867-871.
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