Measuring agreement among participants in group decision-making problems is critical to such processes. This paper introduces a novel consensus index derived from the Gini coefficient, which avoids the need for traditional aggregation matrices, simplifying calculations while maintaining robustness. The proposed Gini Consensus Index demonstrates properties of reciprocity and boundedness, making it a reliable alternative to traditional distance-based measures. Through a comparative statistical analysis using the Wilcoxon test, the GCI performed similarly to established methods but with computational advantages and enhanced stability. These features make it a promising tool for consensus evaluation in fuzzy preference frameworks.

1. [1] E. Herrera-Viedma, F. J. Cabrerizo, J. Kacprzyk, and W. Pedrycz, “A review of soft consensus models in a fuzzy environment,” Information Fusion, Vol.17, pp. 4-13, 2014. https://doi.org/10.1016/j.inffus.2013.04.002
2. [2] H. Zhang, G. Wei, and X. Chen, “SF-GRA method based on cumulative prospect theory for multiple attribute group decision making and its application to emergency supplies supplier selection,” Engineering Applications of Artificial Intelligence, Vol.110, Article No.104679, 2022. https://doi.org/10.1016/j.engappai.2022.104679
3. [3] J. Kacprzyk and M. Fedrizzi, “‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences,” Control and Cybernetics, Vol.15, Nos.3-4, pp. 309-323, 1986.
4. [4] F. J. Cabrerizo, J. M. Moreno, I. J. Pérez, and E. Herrera-Viedma, “Analyzing consensus approaches in fuzzy group decision making: Advantages and drawbacks,” Soft Computing, Vol.14, No.5, pp. 451-463, 2010. https://doi.org/10.1007/s00500-009-0453-x
5. [5] I. J. Pérez, F. J. Cabrerizo, S. Alonso, and E. Herrera-Viedma, “A new consensus model for group decision making problems with non-homogeneous experts,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, Vol.44, No.4, pp. 494-498, 2014. https://doi.org/10.1109/TSMC.2013.2259155
6. [6] S. Zhang, X. Li, and F. Meng, “A distance measure based intuitionistic triangular fuzzy multi-criteria group decision making method and its application,” Applied Intelligence, Vol.53, No.8, pp. 9463-9482, 2023. https://doi.org/10.1007/s10489-022-04009-x
7. [7] F. Chiclana, J. M. T. García, M. J. del Moral, and E. Herrera-Viedma, “A statistical comparative study of different similarity measures of consensus in group decision making,” Information Sciences, Vol.221, pp. 110-123, 2013. https://doi.org/10.1016/j.ins.2012.09.014
8. [8] M. P. Libório, L. M. L. da Silva, P. I. Ekel, L. R. Figueiredo, and P. Bernardes, “Consensus-based sub-indicator weighting approach: Constructing composite indicators compatible with expert opinion,” Social Indicators Research, Vol.164, No.3, pp. 1073-1099, 2022. https://doi.org/10.1007/s11205-022-02989-4
9. [9] X. Dai, H. Li, and L. Zhou, “Consistency and consensus of distributed preference relations based on stochastic optimal allocation in GDM problems,” Group Decision and Negotiation, Vol.33, No.2, pp. 399-437, 2024. https://doi.org/10.1007/s10726-023-09867-5
10. [10] Y. Akiyama, J. Nolan, M. Darrah, M. A. Rahem, and L. Wang, “A method for measuring consensus within groups: An index of disagreement via conditional probability,” Information Sciences, Vol.345, pp. 116-128, 2016. https://doi.org/10.1016/j.ins.2016.01.052
11. [11] M. J. del Moral, F. Chiclana, J. M. T. Garcia, and E. Herrera-Viedma, “An alternative calculation of the consensus degree in group decision making problems,” Procedia Computer Science, Vol.122, pp. 735-742, 2017. https://doi.org/10.1016/j.procs.2017.11.431
12. [12] L. R. Figueiredo, E. A. Frej, G. L. Soares, and P. Y. Ekel, “Group decision-based construction of scenarios for multicriteria analysis in conditions of uncertainty on the basis of quantitative and qualitative information,” Group Decision and Negotiation, Vol.30, No.3, pp. 665-696, 2021. https://doi.org/10.1007/s10726-021-09728-z
13. [13] L. Zhang, Z. Yang, and T. Li, “Group decision making with incomplete interval-valued linguistic intuitionistic fuzzy preference relations,” Information Sciences, Vol.647, Article No.119451, 2023. https://doi.org/10.1016/j.ins.2023.119451
14. [14] M. Li, X. Liu, Y. Xu, and F. Herrera, “An improved multiplicative acceptability consistency-driven group decision making with triangular fuzzy reciprocal preference relations,” Computers & Industrial Engineering, Vol.176, Article No.108981, 2023. https://doi.org/10.1016/j.cie.2023.108981
15. [15] F. Meng, D. Zhao, and X. Zhang, “A fair consensus adjustment mechanism for large-scale group decision making in term of Gini coefficient,” Engineering Applications of Artificial Intelligence, Vol.126, Part C, Article No.106962, 2023. https://doi.org/10.1016/j.engappai.2023.106962
16. [16] S. Goswami, C. A. Murthy, and A. K. Das, “Sparsity measure of a network graph: Gini index,” Information Sciences, Vol.462, pp. 16-39, 2018. https://doi.org/10.1016/j.ins.2018.05.044
17. [17] I. Millet, “The effectiveness of alternative preference elicitation methods in the analytic hierarchy process,” J. of Multi-Criteria Decision Analysis, Vol.6, No.1, pp. 41-51, 1997. https://doi.org/10.1002/(SICI)1099-1360(199701)6:1%3C41::AID-MCDA122%3E3.0.CO;2-D
18. [18] J. Kacprzyk, “Group decision making with a fuzzy linguistic majority,” Fuzzy Sets and Systems, Vol.18, No.2, pp. 105-118, 1986. https://doi.org/10.1016/0165-0114(86)90014-X
19. [19] J. R. Trillo, E. Herrera-Viedma, J. A. Morente-Molinera, and F. J. Cabrerizo, “A group decision-making method based on the experts’ behavior during the debate,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, Vol.53, No.9, pp. 5796-5808, 2023. https://doi.org/10.1109/TSMC.2023.3275056
20. [20] J. R. Trillo, E. Herrera-Viedma, J. A. Morente-Molinera, and F. J. Cabrerizo, “A large scale group decision making system based on sentiment analysis cluster,” Information Fusion, Vol.91, pp. 633-643, 2023. https://doi.org/10.1016/j.inffus.2022.11.009
21. [21] X. Sun, J. Zhu, J. Wang, I. J. Pérez-Gálvez, and F. J. Cabrerizo, “Consensus-reaching process in multi-stage large-scale group decision-making based on social network analysis: Exploring the implication of herding behavior,” Information Fusion, Vol.104, Article No.102184, 2024. https://doi.org/10.1016/j.inffus.2023.102184
22. [22] W. Pedrycz, P. Ekel, and R. Parreiras, “Fuzzy Multicriteria Decision-Making: Models, Methods and Applications,” John Wiley & Sons, 2010.
23. [23] E. Deza and M. M. Deza, “Encyclopedia of Distances,” Springer, 2009. https://doi.org/10.1007/978-3-642-00234-2
24. [24] L. A. Zadeh, “A computational approach to fuzzy quantifiers in natural languages,” N. Cercone (Ed.), “Computational linguistics,” pp. 149-184, Pergamon, 1983. https://doi.org/10.1016/B978-0-08-030253-9.50016-0
25. [25] R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decisionmaking,” IEEE Trans. on Systems, Man, and Cybernetics, Vol.18, No.1, pp. 183-190, 1988. https://doi.org/10.1109/21.87068
26. [26] J. R. Trillo, E. Herrera-Viedma, J. A. Morente-Molinera, and F. J. Cabrerizo, “A group decision-making method based on the experts’ behavior during the debate,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, Vol.53, No.9, pp. 5796-5808, 2023. https://doi.org/10.1109/TSMC.2023.3275056
27. [27] C. Gini, “Variabilità e mutabilità: Contributo allo studio delle distribuzioni e delle relazioni statistiche, Fascicolo 1,” Tipografia di Paolo Cuppini, 1912 (in Italian).
28. [28] J. Haughton and S. R. Khandker, “Handbook on Poverty + Inequality,” The World Bank, 2009.
29. [29] W. J. Tastle and M. J. Wierman, “Consensus and dissention: A measure of ordinal dispersion,” Int. J. of Approximate Reasoning, Vol.45, No.3, pp. 531-545, 2007. https://doi.org/10.1016/j.ijar.2006.06.024
30. [30] M. van den Brakel and R. Lok, “The Robin Hood index adjusted for negatives and equivalised incomes,” J. of Official Statistics, Vol.37, No.4, pp. 1047-1058, 2021. https://doi.org/10.2478/jos-2021-0044
31. [31] D. Alem, A. M. Caunhye, and A. Moreno, “Revisiting Gini for equitable humanitarian logistics,” Socio-Economic Planning Sciences, Vol.82, Article No.101312, 2022. https://doi.org/10.1016/j.seps.2022.101312
32. [32] S. Zhang, X. Dang, D. Nguyen, D. Wilkins, and Y. Chen, “Estimating feature-label dependence using Gini distance statistics,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol.43, No.6, pp. 1947-1963, 2021. https://doi.org/10.1109/TPAMI.2019.2960358
33. [33] T. Miljkovic and Y.-J. Chen, “A new computational approach for estimation of the Gini index based on grouped data,” Computational Statistics, Vol.36, No.3, pp. 2289-2311, 2021. https://doi.org/10.1007/s00180-021-01082-7
34. [34] S. Yitzhaki and E. Schechtman, “The Gini Methodology: A Primer on a Statistical Methodology,” Springer, 2013. https://doi.org/10.1007/978-1-4614-4720-7
35. [35] M. Deveci, I. Gokasar, A. R. Mishra, P. Rani, and Z. Ye, “Evaluation of climate change-resilient transportation alternatives using fuzzy Hamacher aggregation operators based group decision-making model,” Engineering Applications of Artificial Intelligence, Vol.119, Article No.105824, 2023. https://doi.org/10.1016/j.engappai.2023.105824
36. [36] R. Qin, X. Luo, and W. Yang, “Wilcoxon rank test for change in persistence,” Statistics, Vol.55, No.3, pp. 514-531, 2021. https://doi.org/10.1080/02331888.2021.1963964
37. [37] Y. Ouyang, J. Liu, T. Tong, and W. Xu, “A rank-based high-dimensional test for equality of mean vectors,” Computational Statistics & Data Analysis, Vol.173, Article No.107495, 2022. https://doi.org/10.1016/j.csda.2022.107495
38. [38] F. Chiclana, J. M. T. García, M. J. del Moral, and E. Herrera-Viedma, “A statistical comparative study of different similarity measures of consensus in group decision making,” Information Sciences, Vol.221, pp. 110-123, 2013. https://doi.org/10.1016/j.ins.2012.09.014
39. [39] M. J. del Moral, F. Chiclana, J. M. Tapia, and E. Herrera-Viedma, “A comparative study on consensus measures in group decision making,” Int. J. of Intelligent Systems, Vol.33, No.8, pp. 1624-1638, 2018. https://doi.org/10.1002/int.21954
40. [40] J. Xiao, X. Wang, and H. Zhang, “Exploring the ordinal classifications of failure modes in the reliability management: An optimization-based consensus model with bounded confidences,” Group Decision and Negotiation, Vol.31, No.1, pp. 49-80, 2022. https://doi.org/10.1007/s10726-021-09756-9
41. [41] I. J. Navarro, J. V. Martí, and V. Yepes, “Neutrosophic completion technique for incomplete higher-order AHP comparison matrices,” Mathematics, Vol.9, No.5, Article No.496, 2021. https://doi.org/10.3390/math9050496