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A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”

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  • Wang, Zhou-Jing

Abstract

In a recently published paper by Liu et al. [Liu, F., Zhang, W.G., Wang, Z.X. (2012). A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making. European Journal of Operational Research 218, 747–754], two equations are introduced to define consistency of incomplete interval multiplicative preference relations (IMPRs) and employed to develop a goal programming model for estimating missing values. This note illustrates that such consistency definition and estimation model are technically incorrect. New transitivity conditions are proposed to define consistent IMPRs, and a two-stage goal programming approach is devised to estimate missing values for incomplete IMPRs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:247:y:2015:i:3:p:867-871
    DOI: 10.1016/j.ejor.2015.06.015
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    References listed on IDEAS

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    1. Matteo Brunelli & Luisa Canal & Michele Fedrizzi, 2013. "Inconsistency indices for pairwise comparison matrices: a numerical study," Annals of Operations Research, Springer, vol. 211(1), pages 493-509, December.
    2. 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.
    3. 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.
    4. Mattila, V. & Virtanen, K., 2015. "Ranking and selection for multiple performance measures using incomplete preference information," European Journal of Operational Research, Elsevier, vol. 242(2), pages 568-579.
    5. 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.
    6. Punkka, Antti & Salo, Ahti, 2013. "Preference Programming with incomplete ordinal information," European Journal of Operational Research, Elsevier, vol. 231(1), pages 141-150.
    7. 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.
    8. 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.
    9. Liu, Fang & Zhang, Wei-Guo & Wang, Zhong-Xing, 2012. "A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making," European Journal of Operational Research, Elsevier, vol. 218(3), pages 747-754.
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    Citations

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    Cited by:

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    2. Meng, Fanyong & Tan, Chunqiao & Chen, Xiaohong, 2017. "Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study," Omega, Elsevier, vol. 68(C), pages 17-38.
    3. 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.
    4. Qingxian An & Fanyong Meng & Beibei Xiong, 2018. "Interval cross efficiency for fully ranking decision making units using DEA/AHP approach," Annals of Operations Research, Springer, vol. 271(2), pages 297-317, December.
    5. Jaroslav Ramík, 2023. "Deriving priority vector from pairwise comparisons matrix with fuzzy elements by solving optimization problem," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 1045-1062, June.
    6. Liu Fang & Peng Yanan & Zhang Weiguo & Pedrycz Witold, 2017. "On Consistency in AHP and Fuzzy AHP," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 128-147, April.
    7. Jinpei Liu & Jingmiao Song & Qin Xu & Zhifu Tao & Huayou Chen, 2019. "Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 345-370, September.
    8. Jih-Jeng Huang & Chin-Yi Chen, 2024. "A Generalized Method for Deriving Steady-State Behavior of Consistent Fuzzy Priority for Interdependent Criteria," Mathematics, MDPI, vol. 12(18), pages 1-16, September.

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