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The consensus models with interval preference opinions and their economic interpretation

Author

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  • Gong, Zaiwu
  • Xu, Xiaoxia
  • Zhang, Huanhuan
  • Aytun Ozturk, U.
  • Herrera-Viedma, Enrique
  • Xu, Chao

Abstract

This paper aims to explore the case when an individual opinion is interval preference in consensus decision making. And for this purpose, we construct two multi-objective optimization models: one based on the minimum cost from the perspective of the moderator, the other the maximum return from the perspective of the individuals. On the basis of multi-objective programming theories, these multi-objective programming models are then transformed into two single-objective linear programming models, i.e., the primal model and the dual model. The primal model focuses on how to obtain a consensus with the minimum cost, while the dual model is concerned with how to get the maximum return. With the help of dual linear programming theories, we have revealed the following economic significance of the primal-dual consensus models: the primal-dual consensus models can not only help us probe into the relations between the minimum cost paid by the moderator and the maximum return expected by individuals who changed their opinions before, but also help us explore the relations between the unit cost that the moderator pays each individual, unit return that each individual receives, each individual opinion and the consensus opinion. This paper with the aid of theoretical analysis and an illustrative example indicates that once the consensus is obtained, the optimal unit return and optimal consensus opinion value are also solved. This paper also points out that the amount of the total return acquired by all the individuals who have abandoned their original opinions before is equivalent to that of the total cost paid by the moderator to reach the consensus. This paper also argues that there exists compact correlations between the individual׳s unit return, the consensus opinion, the individual׳s interval opinion, and the moderator׳s unit cost.

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  • Gong, Zaiwu & Xu, Xiaoxia & Zhang, Huanhuan & Aytun Ozturk, U. & Herrera-Viedma, Enrique & Xu, Chao, 2015. "The consensus models with interval preference opinions and their economic interpretation," Omega, Elsevier, vol. 55(C), pages 81-90.
    • Handle: RePEc:eee:jomega:v:55:y:2015:i:c:p:81-90
    DOI: 10.1016/j.omega.2015.03.003
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    3. Gong, Zaiwu & Guo, Weiwei & Herrera-Viedma, Enrique & Gong, Zejun & Wei, Guo, 2020. "Consistency and consensus modeling of linear uncertain preference relations," European Journal of Operational Research, Elsevier, vol. 283(1), pages 290-307.
    4. Yuanming Li & Ying Ji & Shaojian Qu, 2022. "Consensus Building for Uncertain Large-Scale Group Decision-Making Based on the Clustering Algorithm and Robust Discrete Optimization," Group Decision and Negotiation, Springer, vol. 31(2), pages 453-489, April.
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    7. 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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    9. Zhang, Huanhuan & Kou, Gang & Peng, Yi, 2019. "Soft consensus cost models for group decision making and economic interpretations," European Journal of Operational Research, Elsevier, vol. 277(3), pages 964-980.
    10. Dong, Yucheng & Liu, Yating & Liang, Haiming & Chiclana, Francisco & Herrera-Viedma, Enrique, 2018. "Strategic weight manipulation in multiple attribute decision making," Omega, Elsevier, vol. 75(C), pages 154-164.
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    13. 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.
    14. 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.
    15. Tang, Ming & Liao, Huchang, 2021. "From conventional group decision making to large-scale group decision making: What are the challenges and how to meet them in big data era? A state-of-the-art survey," Omega, Elsevier, vol. 100(C).
    16. González-Pachón, Jacinto & Romero, Carlos, 2016. "Bentham, Marx and Rawls ethical principles: In search for a compromise," Omega, Elsevier, vol. 62(C), pages 47-51.
    17. 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.
    18. Sha Fan & Hengjie Zhang & Huali Tang, 2019. "A Linguistic Hierarchy Model with Self-Confidence Preference Relations and Its Application in Co-Regulation of Food Safety in China," IJERPH, MDPI, vol. 16(16), pages 1-21, August.
    19. Gong, Zaiwu & Guo, Weiwei & Słowiński, Roman, 2021. "Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction," Omega, Elsevier, vol. 104(C).
    20. Min Xue & Chao Fu & Shan-Lin Yang, 2021. "Dynamic Expert Reliability Based Feedback Mechanism in Consensus Reaching Process with Distributed Preference Relations," Group Decision and Negotiation, Springer, vol. 30(2), pages 341-375, April.
    21. 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.
    22. Shaker Ardakani, Elham & Gilani Larimi, Niloofar & Oveysi Nejad, Maryam & Madani Hosseini, Mahsa & Zargoush, Manaf, 2023. "A resilient, robust transformation of healthcare systems to cope with COVID-19 through alternative resources," Omega, Elsevier, vol. 114(C).
    23. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2019. "Reaching social consensus family budgets: The Spanish case," Omega, Elsevier, vol. 86(C), pages 28-41.
    24. Zaiwu Gong & Lihong Wang, 2017. "On Consistency Test Method of Expert Opinion in Ecological Security Assessment," IJERPH, MDPI, vol. 14(9), pages 1-18, September.

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