IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v306y2023i2p764-776.html
   My bibliography  Save this article

Relationship between the distance consensus and the consensus degree in comprehensive minimum cost consensus models: A polytope-based analysis

Author

Listed:
  • García-Zamora, Diego
  • Dutta, Bapi
  • Massanet, Sebastia
  • Riera, Juan Vicente
  • Martínez, Luis

Abstract

Agreement in Group Decision-Making problems has recently been tackled through the use of Minimum Cost Consensus (MCC) models, which are associated with solving convex optimization problems. Such models minimize the cost of changing experts’ preferences towards reaching a mutual consensus, and establish that the distance between the modified individual preferences and the collective opinion must be bounded by the threshold ε>0. A recent MCC-based model, called the Comprehensive Minimum Cost Consensus (CMCC) model, adds another constraint related to a parameter γ∈[0,1] to the above constraint related to the parameter ε to enforce modified expert preferences in order to achieve a minimum level of agreement dictated by the consensus threshold 1−γ∈[0,1]. This paper attempts to analyze the relationship between the aforementioned constraints in the CMCC models from two different perspectives. The first is based on inequalities and allows simple bounds to be determined to relate the parameters ε and γ. The second one is based on Convex Polytope Theory and provides algorithms that compute more precise bounds to relate these parameters, and could also be applied to other similar optimization problems. Finally, several examples are provided to illustrate the proposal.

Suggested Citation

  • García-Zamora, Diego & Dutta, Bapi & Massanet, Sebastia & Riera, Juan Vicente & Martínez, Luis, 2023. "Relationship between the distance consensus and the consensus degree in comprehensive minimum cost consensus models: A polytope-based analysis," European Journal of Operational Research, Elsevier, vol. 306(2), pages 764-776.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:2:p:764-776
    DOI: 10.1016/j.ejor.2022.08.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722006580
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.08.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Labella, Álvaro & Liu, Hongbin & Rodríguez, Rosa M. & Martínez, Luis, 2020. "A Cost Consensus Metric for Consensus Reaching Processes based on a comprehensive minimum cost model," European Journal of Operational Research, Elsevier, vol. 281(2), pages 316-331.
    3. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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).
    5. Labella, Álvaro & Liu, Hongbin & Rodríguez, Rosa M. & Martínez, Luis, 2020. "A Cost Consensus Metric for Consensus Reaching Processes based on a comprehensive minimum cost model," European Journal of Operational Research, Elsevier, vol. 281(2), pages 316-331.
    6. Xiangrui Chao & Yucheng Dong & Gang Kou & Yi Peng, 2022. "How to determine the consensus threshold in group decision making: a method based on efficiency benchmark using benefit and cost insight," Annals of Operations Research, Springer, vol. 316(1), pages 143-177, September.
    7. Zhen Zhang & Zhuolin Li, 2023. "Consensus-based TOPSIS-Sort-B for multi-criteria sorting in the context of group decision-making," Annals of Operations Research, Springer, vol. 325(2), pages 911-938, June.
    8. Zhang, Bowen & Dong, Yucheng & Zhang, Hengjie & Pedrycz, Witold, 2020. "Consensus mechanism with maximum-return modifications and minimum-cost feedback: A perspective of game theory," European Journal of Operational Research, Elsevier, vol. 287(2), pages 546-559.
    9. 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.
    10. Rodríguez, Rosa M. & Labella, Álvaro & Nuñez-Cacho, Pedro & Molina-Moreno, Valentin & Martínez, Luis, 2022. "A comprehensive minimum cost consensus model for large scale group decision making for circular economy measurement," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    11. Pedro García-del-Valle-y-Durán & Eduardo Gamaliel Hernandez-Martinez & Guillermo Fernández-Anaya, 2022. "The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures," Mathematics, MDPI, vol. 10(20), pages 1-39, October.
    12. Eduardo Fernández & Claudia Gómez-Santillán & Nelson Rangel-Valdez & Laura Cruz-Reyes, 2022. "Group Multi-Objective Optimization Under Imprecision and Uncertainty Using a Novel Interval Outranking Approach," Group Decision and Negotiation, Springer, vol. 31(5), pages 945-994, October.
    13. 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.
    14. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    15. Zhi-Jiao Du & Zhi-Xiang Chen & Su-Min Yu, 2021. "Improved Failure Mode and Effect Analysis: Implementing Risk Assessment and Conflict Risk Mitigation with Probabilistic Linguistic Information," Mathematics, MDPI, vol. 9(11), pages 1-20, May.
    16. 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.
    17. Wu, Xingli & Liao, Huchang, 2019. "A consensus-based probabilistic linguistic gained and lost dominance score method," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1017-1027.
    18. 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.
    19. Wu, Siqi & Wu, Meng & Dong, Yucheng & Liang, Haiming & Zhao, Sihai, 2020. "The 2-rank additive model with axiomatic design in multiple attribute decision making," European Journal of Operational Research, Elsevier, vol. 287(2), pages 536-545.
    20. Yucheng Dong & Yao Li & Ying He & Xia Chen, 2021. "Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 273-295, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:306:y:2023:i:2:p:764-776. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.