The large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets

Yuting Zhu; Wenyu Zhang; Junjie Hou; Hainan Wang; Tingting Wang; Haining Wang; Yuting Zhu; Wenyu Zhang; Junjie Hou; Hainan Wang; Tingting Wang; Haining Wang

doi:10.3934/mbe.2024175

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 3944-3966. doi: 10.3934/mbe.2024175

Previous Article Next Article

Research article

The large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets

1.
China Aerospace Academy of Systems Science and Engineering, Beijing 100048, China
2.
School of Economics and Management, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

Academic Editor:Wei Lin

Received: 30 November 2023 Revised: 13 February 2024 Accepted: 19 February 2024 Published: 22 February 2024

We proposed a novel decision-making method, the large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets, to address the challenge of large-scale group multi-attribute decision-making in fuzzy environments. This method concurrently accounted for the membership and non-membership degrees of decision-making experts in fuzzy environments and the corresponding probabilistic value to quantify expert decision information. Furthermore, it applied to complex scenarios involving groups of 20 or more decision-making experts. We delineated five major steps of the method, elaborating on the specific models and algorithms used in each phase. We began by constructing a probabilistic dual hesitant fuzzy information evaluation matrix and determining attribute weights. The following steps involved classifying large-scale decision-making expert groups and selecting the optimal classification scheme based on effectiveness assessment criteria. A global consensus degree threshold was established, followed by implementing a consensus-reaching model to synchronize opinions within the same class of expert groups. Decision information was integrated within and between classes using an information integration model, leading to a comprehensive decision matrix. Decision outcomes for the objects were then determined through a ranking method. The method's effectiveness and superiority were validated through a case study on urban emergency capability assessment, and its advantages were further emphasized in comparative analyses with other methods.
- probabilistic dual hesitant fuzzy sets,
- large-scale group,
- multi-attribute decision-making,
- group classification model,
- consensus-reaching model
Citation: Yuting Zhu, Wenyu Zhang, Junjie Hou, Hainan Wang, Tingting Wang, Haining Wang. The large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 3944-3966. doi: 10.3934/mbe.2024175

Related Papers:

Abstract

We proposed a novel decision-making method, the large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets, to address the challenge of large-scale group multi-attribute decision-making in fuzzy environments. This method concurrently accounted for the membership and non-membership degrees of decision-making experts in fuzzy environments and the corresponding probabilistic value to quantify expert decision information. Furthermore, it applied to complex scenarios involving groups of 20 or more decision-making experts. We delineated five major steps of the method, elaborating on the specific models and algorithms used in each phase. We began by constructing a probabilistic dual hesitant fuzzy information evaluation matrix and determining attribute weights. The following steps involved classifying large-scale decision-making expert groups and selecting the optimal classification scheme based on effectiveness assessment criteria. A global consensus degree threshold was established, followed by implementing a consensus-reaching model to synchronize opinions within the same class of expert groups. Decision information was integrated within and between classes using an information integration model, leading to a comprehensive decision matrix. Decision outcomes for the objects were then determined through a ranking method. The method's effectiveness and superiority were validated through a case study on urban emergency capability assessment, and its advantages were further emphasized in comparative analyses with other methods.

References

[1]	Q. Ding, Y. M. Wang, M. Goh, TODIM Dynamic emergency decision-making method based on hybrid weighted distance under probabilistic hesitant fuzzy information, Int. J. Fuzzy Syst., 23 (2021), 474–491. https://doi.org/10.1007/s40815-020-00978-8 doi: 10.1007/s40815-020-00978-8
[2]	R. Ikram, S. Meshram, M. Hasan, X. Cao, E. Alvandi, C. Meshram, et al., The application of multi-attribute decision making methods in integrated watershed management, Stochastic Environ. Res. Risk Assess., (2023). https://doi.org/10.1007/s00477-023-02557-3 doi: 10.1007/s00477-023-02557-3
[3]	F. Jin, Y. Zhu, Y. Zhang, S. Guo, J. Liu, L. Zhou, Interval type-2 trapezoidal fuzzy multi-attribute decision-making method and its application to the corporate investment selection, J. Intell. Fuzzy Syst., 45 (2023), 2319–2330. https://doi.org/10.3233/JIFS-230310 doi: 10.3233/JIFS-230310
[4]	Y. Song, G. Li, A mathematical programming approach to manage group decision making with incomplete hesitant fuzzy linguistic preference relations, Comput. Ind. Eng., 135 (2019), 467–475. https://doi.org/10.1016/j.cie.2019.06.036 doi: 10.1016/j.cie.2019.06.036
[5]	Y. Song, G. Li, D. Ergu, N. Liu, An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations, J. Oper. Res. Soc., 73 (2022), 840–854. https://doi.org/10.1080/01605682.2021.1873079 doi: 10.1080/01605682.2021.1873079
[6]	Y. Shen, X. Ma, J. Zhan, A two-stage adaptive consensus reaching model by virtue of three-way clustering for large-scale group decision making, Inf. Sci., 649 (2023), 119658. https://doi.org/10.1016/j.ins.2023.119658 doi: 10.1016/j.ins.2023.119658
[7]	B. Yu, Z. Zheng, Z. Xiao, Y. Fu, Z. Xu, A large-scale group decision-making method based on group-oriented rough dominance relation in scenic spot service improvement, Expert Syst. Appl., 233 (2023), 120999. https://doi.org/10.1016/j.eswa.2023.120999 doi: 10.1016/j.eswa.2023.120999
[8]	F. Meng, D. Zhao, X. Zhang, A fair consensus adjustment mechanism for large-scale group decision making in term of Gini coefficient, Eng. Appl. Artif. Intell., 126 (2023), 106962. https://doi.org/10.1016/j.engappai.2023.106962 doi: 10.1016/j.engappai.2023.106962
[9]	X. Gou, Z. Xu, Double hierarchy linguistic term set and its extensions: The state-of-the-art survey, Int. J. Intell. Syst., 36 (2021), 832–865. https://doi.org/10.1002/int.22323 doi: 10.1002/int.22323
[10]	Y. Shen, X. Ma, J. Zhan, A two-stage adaptive consensus reaching model by virtue of three-way clustering for large-scale group decision making, Inf. Sci., 649 (2023). https://doi.org/10.1016/j.ins.2023.119658 doi: 10.1016/j.ins.2023.119658
[11]	X. Zhou, S. Li, C. Wei, Consensus reaching process for group decision-making based on trust network and ordinal consensus measure, Inf. Fusion, 101 (2024). https://doi.org/10.1016/j.inffus.2023.101969 doi: 10.1016/j.inffus.2023.101969
[12]	S. M. Yu, Z. J. Du, X. Y. Zhang, H. Y. Luo, X. D. Lin, Trust Cop-Kmeans clustering analysis and minimum-cost consensus model considering voluntary trust loss in social network large-scale decision-making, IEEE Trans. Fuzzy Syst., 30 (2022), 2634–2648. https://doi.org/10.1109/TFUZZ.2021.3089745 doi: 10.1109/TFUZZ.2021.3089745
[13]	Y. Li, Y. Ji, S. Qu, Consensus building for uncertain large-scale group decision-making based on the clustering algorithm and robust discrete optimization, Group Decis. Negotiation, 31 (2022), 453–489. https://doi.org/10.1007/s10726-022-09774-1 doi: 10.1007/s10726-022-09774-1
[14]	G. R. Yang, X. Wang, R. X. Ding, S. P. Lin, Q. H. Lou, E. Herrera-Viedma, Managing non-cooperative behaviors in large-scale group decision making based on trust relationships and confidence levels of decision makers, Inf. Fusion, 97 (2023), 101820. https://doi.org/10.1016/j.inffus.2023.101820 doi: 10.1016/j.inffus.2023.101820
[15]	Z. Du, S. Yu, C. Cai, Constrained community detection and multistage multicost consensus in social network large-scale decision-making, IEEE Trans. Comput. Social Syst., (2023). https://doi.org/10.1109/TCSS.2023.3265701 doi: 10.1109/TCSS.2023.3265701
[16]	S. Yu, X. Zhang, Z. Du, Enhanced minimum-cost consensus: focusing on overadjustment and flexible consensus cost, Inf. Fuusion, 89 (2023), 336–354. https://doi.org/10.1016/j.inffus.2022.08.028 doi: 10.1016/j.inffus.2022.08.028
[17]	Z. Chen, X. Zhang, R. Rodriguez, W. Pedrycz, L. Martinez, M.J. Skibniewski, Expertise-structure and risk-appetite-integrated two-tiered collective opinion generation framework for large-scale group decision making, IEEE Trans. Fuzzy Syst., 30 (2022), 5496–5510. https://doi.org/10.1109/TFUZZ.2022.3179594 doi: 10.1109/TFUZZ.2022.3179594
[18]	L. A. Zadeh, Fuzzy logic equals computing with words, IEEE Trans. Fuzzy Syst., 4 (1996), 103–111. https://doi.org/10.1109/91.493904 doi: 10.1109/91.493904
[19]	K. Atanassov, Intuitionistic fuzzy-sets, Fuzzy Sets Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
[20]	R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22 (2014), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989. doi: 10.1109/TFUZZ.2013.2278989
[21]	V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529–539. https://doi.org/10.1002/int.20418 doi: 10.1002/int.20418
[22]	P. Wang, R. Dang, P. Liu, D. Pamucar, Attitude- and cost-driven consistency optimization model for decision-making with probabilistic linguistic preference relation, Comput. Ind. Eng., 186 (2023). https://doi.org/10.1016/j.cie.2023.109748 doi: 10.1016/j.cie.2023.109748
[23]	P. Liu, P. Wang, W. Pedrycz, Consistency-and consensus-based group decision-making method with incomplete probabilistic linguistic preference relations, IEEE Trans. Fuzzy Syst., 29 (2021), 2565–2579. https://doi.org/10.1109/TFUZZ.2020.3003501 doi: 10.1109/TFUZZ.2020.3003501
[24]	Z. Xu, W. Zhou, Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment, Fuzzy Optim. Dec. Making, 16 (2017), 481–503. https://doi.org/10.1007/s10700-016-9257-5 doi: 10.1007/s10700-016-9257-5
[25]	Z. Hao, Z. Xu, H. Zhao, Z. Su, Probabilistic dual hesitant fuzzy set and its application in risk evaluation, Knowledge-Based Syst., 127 (2017), 16–28. https://doi.org/10.1016/j.knosys.2017.02.033 doi: 10.1016/j.knosys.2017.02.033
[26]	Y. Zhu, W. Zhang, J. Hou, R. Zhang, Multi-attribute group decision making algorithm with probabilistic dual hesitant fuzzy sets and PROMETHEE method, Comput. Eng. Appl., 58 (2022), 88–97. https://doi.org/10.3778/j.issn.1002-8331.2203-0483 doi: 10.3778/j.issn.1002-8331.2203-0483
[27]	B. Ning, H. Wang, G. Wei, C. Wei, Several similarity measures of probabilistic dual hesitant fuzzy sets and their applications to new energy vehicle charging station location, Alexandria Eng. J., 71 (2023), 371–385. https://doi.org/10.1016/j.aej.2023.03.052 doi: 10.1016/j.aej.2023.03.052
[28]	W. Zhang, Y. Zhu, The probabilistic dual hesitant fuzzy multi-attribute decision-making method based on cumulative prospect theory and its application, Axioms, 12 (2023). https://doi.org/10.3390/axioms12100925 doi: 10.3390/axioms12100925
[29]	Z. Ren, Z. Xu, H. Wang, The strategy selection problem on artificial intelligence with an integrated VIKOR and AHP method under probabilistic dual hesitant fuzzy information, IEEE Access, 7 (2019), 103979–103999. https://doi.org/10.1109/ACCESS.2019.2931405 doi: 10.1109/ACCESS.2019.2931405
[30]	X. Wang, H. Wang, Z. Xu, Z. Ren, Green supplier selection based on probabilistic dual hesitant fuzzy sets: A process integrating best worst method and superiority and inferiority ranking, Appl. Intell., 52 (2022), 8279–8301. https://doi.org/10.1007/s10489-021-02821-5 doi: 10.1007/s10489-021-02821-5
[31]	H. Li, F. Li, J. Zuo, J. Sun, C. Yuan, L. Ji, et al., Emergency decision-making system for the large-scale infrastructure: a case study of the south-to-north water diversion project, J. Infrastruct. Syst., 28 (2022). https://doi.org/10.1061/(ASCE)IS.1943-555X.0000659 doi: 10.1061/(ASCE)IS.1943-555X.0000659
[32]	X. Gou, Z. Xu, H. Liao, F. Herrera, Consensus model handling minority opinions and noncooperative behaviors in large-scale group decision-making under double hierarchy linguistic preference relations, IEEE Trans. Cybern., 51 (2021), 283–296. https://doi.org/10.1109/TCYB.2020.2985069 doi: 10.1109/TCYB.2020.2985069
[33]	A. Aydogdu, S. Gul, New entropy propositions for interval-valued spherical fuzzy sets and their usage in an extension of ARAS (ARAS-IVSFS), Expert Syst., 39 (2022). https://doi.org/10.1111/exsy.12898 doi: 10.1111/exsy.12898
[34]	H. Garg, T. Mahmood, U. ur Rehman, Z. Ali, CHFS: Complex hesitant fuzzy sets-their applications to decision making with different and innovative distance measures, CAAI Trans. Intell. Technol., 6 (2021), 93–122. https://doi.org/10.1049/cit2.12016 doi: 10.1049/cit2.12016
[35]	Z. Ma, J. Zhu, S. Zhang, H. Wang, X. Liu, Classification-based aggregation model on large scale group decision making with hesitant fuzzy linguistic information, J. Control Decis., 34 (2019), 167–179.
[36]	L. Wang, H. Xue, Group decision-making method based on expert classification consensus information integration, Symmetry, 12 (2020), 1180. https://doi.org/10.3390/sym12071180 doi: 10.3390/sym12071180
[37]	H. Hassani, R. Razavi-Far, M. Saif, E. Herrera-Viedma, Consensus-based decision support model and fusion architecture for dynamic decision making, Inf. Sci., 597 (2022), 86–104. https://doi.org/10.1016/j.ins.2022.03.040 doi: 10.1016/j.ins.2022.03.040
[38]	K. Qi, H. Chai, Q. Duan, Y. Du, Q. Wang, J. Sun, et al., A collaborative emergency decision making approach based on BWM and TODIM under interval 2-tuple linguistic environment, Int. J. Mach. Learn. Cybern., 13 (2022), 383–405. https://doi.org/10.1007/s13042-021-01412-7 doi: 10.1007/s13042-021-01412-7
[39]	S. Zhang, X. Liu, J. Zhu, and Z. Wang, Adaptive consensus model with hesitant fuzzy linguistic information considering individual cumulative consensus contribution, J. Control Decis., 36 (2021), 187–195.
[40]	H. Garg, G. Kaur, Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information, Comput. Ind. Eng., 140 (2020). https://doi.org/10.1016/j.cie.2019.106211 doi: 10.1016/j.cie.2019.106211
[41]	Z. Wu, J. Xu, A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters, Inf. Fusion, 41 (2018), 217–231. https://doi.org/10.1016/j.inffus.2017.09.011 doi: 10.1016/j.inffus.2017.09.011

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)