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Consensus measures based on a fuzzy concept

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  • Dombi, József
  • Jónás, Tamás

Abstract

When evaluations concerning a decision alternative are available from multiple sources (e.g. criteria or experts), the individual evaluation inputs are typically combined into one value that may be viewed as an aggregate evaluation of the alternative. In such situations, besides the aggregate value, the extent to which the inputs agree is also an important piece of information. Consensus measures are utilized for measuring this degree of agreement. In our study, we will introduce the so-called decumulative distribution function of the individual inputs measured on the unit interval. Using a fuzziness measure of this function, we will construct a consensus measure that satisfies seven reasonable properties. In the proposed construction, a consensus measure depends on a fuzzy entropy that may be viewed as the generator of the proposed consensus measure. This generator function-based nature of the proposed consensus measure makes it flexible. Also, we will prove that in a special case, the new consensus measure coincides with the measure of Bonferroni consensus with implication pairs. Furthermore, we will describe how our proposal can be extended to a weighted version.

Suggested Citation

  • Dombi, József & Jónás, Tamás, 2024. "Consensus measures based on a fuzzy concept," European Journal of Operational Research, Elsevier, vol. 315(2), pages 642-653.
    • Handle: RePEc:eee:ejores:v:315:y:2024:i:2:p:642-653
    DOI: 10.1016/j.ejor.2024.01.004
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    References listed on IDEAS

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    1. 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.
    2. 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).
    3. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    4. Mario Fedrizzi & Michele Fedrizzi & Ricardo Alberto Marques Pereira & Matteo Brunelli, 2010. "The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences," DISA Working Papers 1004, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2010.
    5. Eklund, Patrik & Rusinowska, Agnieszka & De Swart, Harrie, 2007. "Consensus reaching in committees," European Journal of Operational Research, Elsevier, vol. 178(1), pages 185-193, April.
    6. Li, Yanhong & Kou, Gang & Li, Guangxu & Peng, Yi, 2022. "Consensus reaching process in large-scale group decision making based on bounded confidence and social network," European Journal of Operational Research, Elsevier, vol. 303(2), pages 790-802.
    7. 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.
    8. F. J. Cabrerizo & S. Alonso & E. Herrera-Viedma, 2009. "A Consensus Model For Group Decision Making Problems With Unbalanced Fuzzy Linguistic Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 109-131.
    9. 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.
    10. Tang, Ming & Liao, Huchang & Mi, Xiaomei & Lev, Benjamin & Pedrycz, Witold, 2021. "A hierarchical consensus reaching process for group decision making with noncooperative behaviors," European Journal of Operational Research, Elsevier, vol. 293(2), pages 632-642.
    11. 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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    Cited by:

    1. Tang, Jie & Li, Zi-Jun & Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold, 2025. "Biform game consensus analysis of group decision making with unconnected social network," European Journal of Operational Research, Elsevier, vol. 324(1), pages 259-275.
    2. József Dombi & Jenő Fáró & Tamás Jónás, 2025. "A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers," Mathematics, MDPI, vol. 13(3), pages 1-24, February.
    3. Wen, Tao & Zheng, Rui & Wu, Ting & Liu, Zeyi & Zhou, Mi & Syed, Tahir Abbas & Ghataoura, Darminder & Chen, Yu-wang, 2025. "Formulating opinion dynamics from belief formation, diffusion and updating in social network group decision-making: Towards developing a holistic framework," European Journal of Operational Research, Elsevier, vol. 325(3), pages 381-399.

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