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Multi-stage optimization models for individual consistency and group consensus with preference relations

Author

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  • Wu, Zhibin
  • Huang, Shuai
  • Xu, Jiuping

Abstract

In this paper, a systematic optimization framework is developed to address the individual consistency and group consensus issues in decision making problems that involve human judgment for which pairwise comparisons are frequently adopted. In existing optimization approaches, the modified preferences have been limited to continuous numerical terms, and the uniqueness of these models has not been explicitly addressed. To resolve these issues, in this paper, two frameworks are developed; one to improve individual level consistency and the other to achieve group level consensus. Using discrete scales, the proposed models are proven to have equivalent integer linear programming forms that can be solved using a sequential optimization strategy in which the size of the change, the number of modifications, and the number of individuals who need to revise their preferences are sequentially optimized. To enhance the acceptability of the suggested preferences, an interactive consistency process and interactive consensus process based on the multi-stage models are also designed. Numerical examples are presented to illustrate the developed approaches.

Suggested Citation

  • Wu, Zhibin & Huang, Shuai & Xu, Jiuping, 2019. "Multi-stage optimization models for individual consistency and group consensus with preference relations," European Journal of Operational Research, Elsevier, vol. 275(1), pages 182-194.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:1:p:182-194
    DOI: 10.1016/j.ejor.2018.11.014
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    1. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
    2. 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.
    3. Gong, Zaiwu & Zhang, Huanhuan & Forrest, Jeffrey & Li, Lianshui & Xu, Xiaoxia, 2015. "Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual," European Journal of Operational Research, Elsevier, vol. 240(1), pages 183-192.
    4. Fedrizzi, Michele & Giove, Silvio, 2007. "Incomplete pairwise comparison and consistency optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 303-313, November.
    5. Wu, Zhibin & Xu, Jiuping, 2016. "Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations," Omega, Elsevier, vol. 65(C), pages 28-40.
    6. Franco, L. Alberto & Rouwette, Etiënne A.J.A. & Korzilius, Hubert, 2016. "Different paths to consensus? The impact of need for closure on model-supported group conflict management," European Journal of Operational Research, Elsevier, vol. 249(3), pages 878-889.
    7. 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.
    8. Kacprzyk, Janusz & Fedrizzi, Mario, 1988. "A `soft' measure of consensus in the setting of partial (fuzzy) preferences," European Journal of Operational Research, Elsevier, vol. 34(3), pages 316-325, March.
    9. Dong, Qingxing & Cooper, Orrin, 2016. "A peer-to-peer dynamic adaptive consensus reaching model for the group AHP decision making," European Journal of Operational Research, Elsevier, vol. 250(2), pages 521-530.
    10. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    11. Dalal, Reeshad S. & Bonaccio, Silvia, 2010. "What types of advice do decision-makers prefer?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 112(1), pages 11-23, May.
    12. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    13. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    14. Herrera, F. & Herrera-Viedma, E. & Chiclana, F., 2001. "Multiperson decision-making based on multiplicative preference relations," European Journal of Operational Research, Elsevier, vol. 129(2), pages 372-385, March.
    15. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    16. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    17. Valdecy Pereira & Helder Costa, 2015. "Nonlinear programming applied to the reduction of inconsistency in the AHP method," Annals of Operations Research, Springer, vol. 229(1), pages 635-655, June.
    18. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
    19. Reimann, Olivier & Schumacher, Christian & Vetschera, Rudolf, 2017. "How well does the OWA operator represent real preferences?," European Journal of Operational Research, Elsevier, vol. 258(3), pages 993-1003.
    20. Gleb Beliakov & Simon James & Tim Wilkin, 2017. "Aggregation and consensus for preference relations based on fuzzy partial orders," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 409-428, December.
    21. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Feng, Bo, 2010. "The OWA-based consensus operator under linguistic representation models using position indexes," European Journal of Operational Research, Elsevier, vol. 203(2), pages 455-463, June.
    22. Fan, Zhi-Ping & Ma, Jian & Jiang, Yan-Ping & Sun, Yong-Hong & Ma, Louis, 2006. "A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 174(1), pages 311-321, October.
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    Cited by:

    1. Zhibin Wu & Jie Xiao & Ivan Palomares, 2019. "Direct Iterative Procedures for Consensus Building with Additive Preference Relations Based on the Discrete Assessment Scale," Group Decision and Negotiation, Springer, vol. 28(6), pages 1167-1191, December.
    2. Cheng, Dong & Yuan, Yuxiang & Wu, Yong & Hao, Tiantian & Cheng, Faxin, 2022. "Maximum satisfaction consensus with budget constraints considering individual tolerance and compromise limit behaviors," European Journal of Operational Research, Elsevier, vol. 297(1), pages 221-238.
    3. Kang Xu & Jiuping Xu, 2020. "A direct consistency test and improvement method for the analytic hierarchy process," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 359-388, September.
    4. Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold & Chu, Jun-Fei, 2023. "Selfish-dilemma consensus analysis for group decision making in the perspective of cooperative game theory," European Journal of Operational Research, Elsevier, vol. 308(1), pages 290-305.
    5. Guo, Weiwei & Gong, Zaiwu & Zhang, Wei-Guo & Xu, Yanxin, 2023. "Minimum cost consensus modeling under dynamic feedback regulation mechanism considering consensus principle and tolerance level," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1279-1295.

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