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A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

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  • Wang, Zhou-Jing
  • Li, Kevin W.

Abstract

This article presents a goal programming framework to solve group decision making problems where decision-makers’ judgments are provided as incomplete interval additive reciprocal comparison matrices (IARCMs). New properties of multiplicative consistent IARCMs are put forward and used to define consistent incomplete IARCMs. A two-step goal programming method is developed to estimate missing values for an incomplete IARCM. The first step minimizes the inconsistency of the completed IARCMs and controls uncertainty ratios of the estimated judgments within an acceptable threshold, and the second step finds the most appropriate estimated missing values among the optimal solutions obtained from the previous step. A weighted geometric mean approach is proposed to aggregate individual IARCMs into a group IARCM by employing the lower bounds of the interval additive reciprocal judgments. A two-step procedure consisting of two goal programming models is established to derive interval weights from the group IARCM. The first model is devised to minimize the absolute difference between the logarithm of the group preference and that of the constructed multiplicative consistent judgment. The second model is developed to generate an interval-valued priority vector by maximizing the uncertainty ratio of the constructed consistent IARCM and incorporating the optimal objective value of the first model as a constraint. Two numerical examples are furnished to demonstrate validity and applicability of the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:242:y:2015:i:3:p:890-900
    DOI: 10.1016/j.ejor.2014.10.025
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    1. 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.
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    3. Xiaodong Yu & Atiq ur Rehman & Samina Ashraf & Muhammad Hussain & Shahzad Faizi, 2023. "Multiperson Decision-Making Using Consistent Interval-Valued Fuzzy Information with Application in Supplier Selection," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    4. Jones, Dylan & Florentino, Helenice & Cantane, Daniela & Oliveira, Rogerio, 2016. "An extended goal programming methodology for analysis of a network encompassing multiple objectives and stakeholders," European Journal of Operational Research, Elsevier, vol. 255(3), pages 845-855.
    5. 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.
    6. 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.
    7. Hanks, Robert W. & Weir, Jeffery D. & Lunday, Brian J., 2017. "Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 262(2), pages 636-646.
    8. 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.
    9. Yong Liu & Ting Zhou & Wei-xue Diao & Jinhong Yi, 2022. "A multivariate minimum cost consensus approach for two-level group decision making," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 839-861, September.
    10. Fu, Chao & Yang, Jian-Bo & Yang, Shan-Lin, 2015. "A group evidential reasoning approach based on expert reliability," European Journal of Operational Research, Elsevier, vol. 246(3), pages 886-893.
    11. Lidan Pei & Feifei Jin & Zhiwei Ni & Huayou Chen & Zhifu Tao, 2017. "An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2779-2793, October.
    12. Yong Liu & Ting Zhou & Jeffrey Yi-Lin Forrest, 2020. "A Multivariate Minimum Cost Consensus Model for Negotiations of Holdout Demolition," Group Decision and Negotiation, Springer, vol. 29(5), pages 871-899, October.

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