Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management
Abstract
:1. Introduction
- (1)
- The existing research on LSGDM rarely considers the large-scale contexts of hundreds or thousands of decision makers (DMs).
- (2)
- From the perspective of preference information loss, there is currently no LSGDM framework specifically targeting a consensus-reaching process (CRP) in the context of multi-granular linguistic information.
2. Preliminaries
2.1. Representation Model for Language and Multi-Granular Linguistic Information
2.1.1. Representation Model for Language
2.1.2. Multi-Granularity Language Representation Model
2.2. Preference Relations: LPR and PLPR and Their Definitions of Consistency
3. LSGDM with Public Participation Based on MG-PLPRs
3.1. Consistency of PLPR
3.2. Determination of Subgroup Weight
- (1)
- It is assumed that decision makers have the same importance, in which case the weight of the subgroup from DMs who put to use the linguistic term set is
- (2)
- Let us say there are decision makers with different levels of importance. Let represent the personal importance of the DMs , where , and . Then, the weight of the subgroup from DMs who use the linguistic term set is
3.3. Group Consensus Degree
3.4. An Optimization Model-Based CRP with MG-PLPRs
3.5. A Step by Step Procedure of the LSGDM with Public Participation Based on MG-PLPRs
4. Case Studies and Comparative Analysis
4.1. The Siting of “Shared Garden”
4.2. Comparative Analysis
- (1)
- Compared with the methods based on Operator
- (2)
- Compared with the related CRP method [28]
5. Discussion
- (1)
- Comparative analysis with existing LSGDM methods.
- (i)
- Comparison with consensus models [24,47,48]: In GDM, CRP can be divided into two categories: the interactions and the automatic mechanism, based on whether DMs are involved in the consensus process. Gou et al. [24] developed a feedback-adjustment rules-based CRP for LSGDM with double-hierarchy-hesitant fuzzy linguistic preference relations. Zhang et al. [47] proposed an iterative-CRP model based on hesitant fuzzy preference relations. The iteration-based CRP consists of two main steps: The first step is individual consensus improvement, and the second step is group consensus improvement. In environments where hundreds or thousands of DMs are involved, feedback mechanisms involving mediators are obsolete because they are too time-consuming and impractical in practice [10]. Therefore, CRP in LSGDM is committed to implementation with automatic mechanisms. In particular, automatic consensus models based on mathematical optimization techniques have been widely expanded [10,48].Compared to these two typical group consensus models [24,47,48], we proposed an optimization-based CRP in LSGDM to manage multi-granular linguistic terms set and obtained satisfactory individual consistency and group consensus at the same time, which reduces the preference information loss as much as possible and enhances its application in practice.
- (ii)
- Comparison with LSGDM methods using multi-granular linguistic terms set [28,46]: Zhang et al. [46] developed a large-scale multi-attribute group-decision-making method using multigranular linguistic distribution assessments. However, this article does not consider group consensus-reaching. Moreover, Song and Li [28] proposed an LSGDM method with multi-granular probabilistic 2-tuple fuzzy linguistic preference relations. In this study, an automatic iteration CRP was established.
- (2)
- Scalability of the proposed methods.
6. Conclusions
- We propose an LSGDM method with public participation, which allows hundreds or thousands of DMs to participate and is practical in practical applications.
- An optimization-based CRP with MG-PLPRs in an LGDM problem is proposed, which does not need to carry out uniform granularity processing on MG-PLPRs and can directly obtain the priority weight vector of alternative schemes while ensuring a satisfactory level of personality consistency and group consensus, which not only avoids information loss but also reduces computational complexity.
- A city “shared garden” site selection is solved through the LSGDM method of public participation established in this paper. A total of 100 representative owners participated in the decision-making process, and the final site selection meets the views of the majority of the public and has good applicability.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Brombal, D.; Moriggi, A.; Marcomini, A. Evaluating public participation in Chinese, E.I.A. An integrated Public Participation Index and its application to the case of the New Beijing Airport. Environ. Impact Assess. Rev. 2017, 62, 49–60. [Google Scholar] [CrossRef]
- Liang, H.; Ren, J.; Lin, R.; Liu, Y. Alternative-fuel based vehicles for sustainable transportation: A fuzzy group decision supporting framework for sustainability prioritization. Technol. Forecast. Soc. Chang. 2019, 140, 33–43. [Google Scholar] [CrossRef]
- Thomas, J. Public participation in public decisions. Gov. Fin. Rev. 1995, 35, 689–694. [Google Scholar]
- Tse, H.; Lam, C.; Gu, J.; Lin, X. Examining the interpersonal process and consequence of leader–member exchange comparison: The role of procedural justice climate. J. Organ. Behav. 2018, 39, 922–940. [Google Scholar] [CrossRef]
- You, X.; Hou, F.; Chiclana, F. Consensus reaching process with noncooperative behaviors in large-scale group social network environment. Appl. Soft Comput. 2023, 144, 110454. [Google Scholar] [CrossRef]
- Li, G.X.; Kou, G.; Peng, Y. Heterogeneous large-scale group decision making using fuzzy cluster analysis and its application to emergency response plan selection. IEEE Trans. Syst. Man Cybern. Syst. 2022, 52, 3391–3403. [Google Scholar] [CrossRef]
- Zhang, X.; Meng, F. A large-scale group decision making method to select the ideal mobile health application for the hospital. Appl. Intell. 2022, 52, 15844–15864. [Google Scholar] [CrossRef] [PubMed]
- Zhang, H.J.; Xiao, J.; Palomares, I.; Liang, H.M.; Dong, Y.C. Linguistic distribution-based optimization approach for large-scale GDM with comparative linguistic information: An application on the selection of wastewater disinfection technology. IEEE Trans. Fuzzy Syst. 2020, 28, 376–389. [Google Scholar] [CrossRef]
- Mahmoudi, A.; Abbasi, M.; Yuan, J.; Li, L. Large-scale group decision-making (LSGDM) for performance measurement of healthcare construction projects: Ordinal Priority Approach. Appl. Intell. 2022, 52, 13781–13802. [Google Scholar] [CrossRef] [PubMed]
- García-Zamora, D.; Labella, Á.; Ding, W.; Rodríguez, R.M.; Martínez, L. Large-Scale Group Decision Making: A Systematic Review and a Critical Analysis. IEEE/CAA J. Autom. Sin. 2022, 9, 949–966. [Google Scholar] [CrossRef]
- Liu, P.; Wang, X.; Teng, F.; Li, Y.; Wang, F. Distance education quality evaluation based on multigranularity probabilistic linguistic term sets and disappointment theory. Inf. Sci. 2022, 605, 159–181. [Google Scholar] [CrossRef]
- Liang, Y.; Ju, Y.; Qin, J.; Pedrycz, W. Multi-granular linguistic distribution evidential reasoning method for renewable energy project risk assessment. Inf. Fusion 2021, 65, 147–164. [Google Scholar] [CrossRef]
- Han, Y.J.; Cao, M.M.; Liu, H.C. New approach for quality function deployment based on multi-granular unbalanced linguistic information and consensus reaching process. Appl. Soft Comput. 2023, 144, 110490. [Google Scholar] [CrossRef]
- Song, Y.M.; Li, G.X. A large-scale group decision making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection. J. Oper. Res. Soc. 2019, 70, 827–841. [Google Scholar] [CrossRef]
- Morente-Molinera, J.A.; Pérez, I.J.; Ureña, M.R.; Herrera-Viedma, E. On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends. Knowl. Based Syst. 2015, 74, 49–60. [Google Scholar] [CrossRef]
- Zhang, Z.; Li, Z.; Gao, Y. Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach. Inf. Fusion 2021, 74, 96–110. [Google Scholar] [CrossRef]
- Pang, Q.; Wang, H.; Xu, Z.S. Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 2016, 369, 128–143. [Google Scholar] [CrossRef]
- Song, Y.M.; Hu, J. Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation. Appl. Soft Comput. 2019, 80, 712–722. [Google Scholar] [CrossRef]
- Palomares, I.; Martínez, L.; Herrera, F. A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Trans. Fuzzy Syst. 2014, 22, 516–530. [Google Scholar] [CrossRef]
- Dong, Y.C.; Zha, Q.B.; Zhang, H.J.; Kou, G.; Fujita, H.; Chiclana, F.; Herrera-Viedma, E. Consensus reaching in social network group decision making: Research paradigms and challenges. Knowl. Based Syst. 2018, 162, 3–13. [Google Scholar] [CrossRef]
- Wang, R.; Chen, Z.S.; Shuai, B.; Martínez, L.; Kong, W.T.; Pedrycz, W. Revisiting the consistency improvement and consensus reaching processes of intuitionistic multiplicative preference relations. Eng. Appl. Artif. Intell. 2023, 120, 105931. [Google Scholar] [CrossRef]
- Wu, G.; Zhang, W.; Wu, Z. Local minimum adjustment for the consensus model with distribution linguistic preference relations considering preference reliability. Inf. Fusion 2023, 93, 21–35. [Google Scholar] [CrossRef]
- Rodríguez, R.M.; Labella, A.; Sesma-Sara, M.; Bustince, H.; Martínez, L. A cohesion-driven consensus reaching process for large scale group decision making under a hesitant fuzzy linguistic term sets environment. Comput. Ind. Eng. 2021, 155, 107158. [Google Scholar] [CrossRef]
- Gou, X.; Xu, Z.; Herrera, F. Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowl. Based Syst. 2018, 157, 20–33. [Google Scholar] [CrossRef]
- Wan, S.; Yan, J.; Dong, J. Personalized individual semantics based consensus reaching process for large-scale group decision making with probabilistic linguistic preference relations and application to COVID-19 surveillance. Expert Syst. Appl. 2022, 191, 116328. [Google Scholar] [CrossRef]
- Gai, T.; Cao, M.; Chiclana, F.; Wu, J.; Liang, C.; Herrera-Viedma, E. A decentralized feedback mechanism with compromise behavior for large-scale group consensus reaching process with application in smart logistics supplier selection. Expert Syst. Appl. 2022, 204, 117547. [Google Scholar] [CrossRef]
- Zhou, M.; Zheng, Y.Q.; Chen, Y.W.; Cheng, B.Y.; Herrera-Viedma, E.; Wu, J. A large-scale group consensus reaching approach considering self-confidence with two-tuple linguistic trust/distrust relationship and its application in life cycle sustainability assessment. Inf. Fusion 2023, 94, 181–199. [Google Scholar] [CrossRef]
- Song, Y.M.; Li, G.X. Consensus constructing in large-scale group decision making with multi-granular probabilistic 2-tuple fuzzy linguistic preference relations. IEEE Access 2019, 7, 56947–56959. [Google Scholar] [CrossRef]
- Liu, Y.; Yang, Y.; Sun, L.; Huang, A. Managing multi-granular probabilistic linguistic information in large-scale group decision making: A personalized individual semantics-based consensus model. Expert Syst. Appl. 2023, 230, 120645. [Google Scholar] [CrossRef]
- Zhang, H.; Dong, Y.; Chiclana, F.; Yu, S. Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design. Eur. J. Oper. Res. 2019, 275, 580–598. [Google Scholar] [CrossRef]
- Liao, H.; Wu, Z.; Tang, M.; Wan, Z. An interactive consensus reaching model with updated weights of clusters in large-scale group decision making. Eng. Appl. Artif. Intell. 2022, 107, 104532. [Google Scholar] [CrossRef]
- Li, Y.; Kou, G.; Li, G.; Peng, Y. Consensus reaching process in large-scale group decision making based on bounded confidence and social network. Eur. J. Oper. Res. 2022, 303, 790–802. [Google Scholar] [CrossRef]
- Ben-Arieh, D.; Easton, T. Multi-criteria group consensus under linear cost opinion elasticity. Decis. Support Syst. 2007, 43, 713–721. [Google Scholar] [CrossRef]
- Dong, Y.; Xu, Y.; Li, H.; Feng, B. The OWA-based consensus operator under lin- guistic representation models using position indexes. Eur. J. Oper. Res. 2010, 203, 455–463. [Google Scholar] [CrossRef]
- Song, Y.M.; Li, G.X.; Ergu, D.; Liu, N. An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations. J. Oper. Res. Soc. 2022, 73, 840–854. [Google Scholar] [CrossRef]
- Zhang, H.; Zhao, S.; Kou, G.; Li, C.C.; Dong, Y.; Herrera, F. An overview on feedback mechanisms with minimum adjustment or cost in consensus reaching in group decision making: Research paradigms and challenges. Inf. Fusion 2020, 60, 65–79. [Google Scholar] [CrossRef]
- Herrera, F.; Martínez, L. A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 2000, 8, 746–752. [Google Scholar]
- Xu, Z.S. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 2004, 166, 19–30. [Google Scholar] [CrossRef]
- Herrera-Viedma, E.; Martínez, L.; Mata, F.; Chiclana, F. A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Trans. Fuzzy Syst. 2005, 13, 644–658. [Google Scholar] [CrossRef]
- Jin, F.; Ni, Z.; Chen, H.; Li, Y. Approaches to decision making with linguistic preference relations based on additive consistency. Appl. Soft Comput. 2016, 49, 71–80. [Google Scholar] [CrossRef]
- Zhang, Y.; Xu, Z.; Wang, H.; Liao, H.C. Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput. 2016, 49, 817–833. [Google Scholar] [CrossRef]
- Liu, P.D.; Gao, H.; Ma, J. Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. Inf. Sci. 2019, 490, 292–316. [Google Scholar] [CrossRef]
- Herrera-Viedma, E.; Cabrerizo, F.J.; Kacprzyk, J.; Pedrycz, W. A review of soft consensus models in a fuzzy environment. Inf. Fusion 2014, 17, 4–13. [Google Scholar] [CrossRef]
- Espinilla, M.; Liu, J.; Martínez, L. An extended hierarchical linguistic model for decision-making problems. Comput. Intell. 2011, 27, 489–512. [Google Scholar] [CrossRef]
- Zhang, G.; Dong, Y.; Xu, Y. Consistency and consensus measures for linguistic preference relations based on distribution assessments. Inf. Fusion 2014, 17, 46–55. [Google Scholar] [CrossRef]
- Zhang, Z.; Guo, C.H.; Martínez, L. Managing multigranular linguistic distribution assessments in large-scale multiattribute group decision making. IEEE Trans. Syst. Man Cybern. Syst. 2017, 47, 3063–3076. [Google Scholar] [CrossRef]
- Zhang, Z.; Wang, C.; Tian, X. A decision support model for group decision making with hesitant fuzzy preference relations. Knowl. Based Syst. 2015, 86, 77–101. [Google Scholar] [CrossRef]
- Xiao, J.; Wang, X.; Zhang, H. Managing personalized individual semantics and consensus in linguistic distribution large-scale group decision making. Inf. Fusion 2020, 53, 20–34. [Google Scholar] [CrossRef]
Studies | Whether to Consider CRP | The Method of CRP | Ranking |
---|---|---|---|
The proposed method | Yes | Optimization model-based CRP method | |
Operator-based approach | No | / | |
Song and Li [28] | Yes | An automatic iteration-based CRP method |
\ | ||||
\ | \ | |||
\ | \ | \ |
\ | ||||
\ | \ | |||
\ | \ | \ |
\ | ||||
\ | \ | |||
\ | \ | \ |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Niu, X.; Song, Y.; Xu, Z. Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management. Mathematics 2024, 12, 2528. https://doi.org/10.3390/math12162528
Niu X, Song Y, Xu Z. Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management. Mathematics. 2024; 12(16):2528. https://doi.org/10.3390/math12162528
Chicago/Turabian StyleNiu, Xiuhong, Yongming Song, and Zhongwen Xu. 2024. "Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management" Mathematics 12, no. 16: 2528. https://doi.org/10.3390/math12162528