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A Novel Consensus and Dissent Framework Under Grey Preference Based on the Graph Model for Conflict Resolution for Two Decision Makers

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Abstract

The existing consensus models of conflict decision-making generally assume that the decision-makers’ preferences are simple and certain. This assumption oversimplifies the complexity of real-world conflicts due to the ignorance of the decision-maker’s limited rationality. The present work makes the first attempt at solving this issue by defining the grey consensus and dissent preference of two decision makers (DMs), which is then embedded into the Graph Model for Conflict Resolution (GMCR) to obtain conflict equilibrium solutions. To be specific, preference relations are first described as interval grey scales to reflect the decision maker’s judgments on conflict states, and then converted into crisp values to interface with GMCR. We next present both the logical and matrix representations under the GMCR framework, along with detailed pseudocode that can be implemented to investigate actual conflict situations practically. For validation and verification purposes, the proposed decision framework is applied to the water resource conflict of the Yellow River Basin in China, from which insights are derived to facilitate effective strategic decision-making for resolving complex conflicts in uncertain environments.

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Notes

  1. In this work, we use “he” to indicate DM i and “she” for DM j.

References

  • Ben-Haim Y, Hipel KW (2002) The graph model for conflict resolution with information-gap uncertainty in preferences. Appl Math Comput 126(2–3):319–340

    Google Scholar 

  • Bennett PG (1980) Hypergames: developing a model of conflict. Futures 12(6):489–507

    Article  Google Scholar 

  • Chen X, Zhang W, Xu X, Cao W (2022) Managing group confidence and consensus in intuitionistic fuzzy large group decision-making based on social media data mining. Group Decis Negot 31(5):995–1023

    Article  Google Scholar 

  • Deng J (1989) Introduction to grey system theory. J Grey Syst 1(1):1–24

    Google Scholar 

  • Fang L, Hipel KW, Kilgour DM (1993) Interactive decision making: the graph model for conflict resolution, vol 11. John Wiley & Sons, New Jersey

    Google Scholar 

  • Fang L, Hipel KW, Kilgour DM, Peng X (2003) A decision support system for interactive decision making-part i: model formulation. IEEE Trans Syst Man Cybern Part C (Appl Rev) 33(1):42–55

    Article  Google Scholar 

  • Fang L, Hipel KW, Kilgour DM, Peng X (2003) A decision support system for interactive decision making-part ii: analysis and output interpretation. IEEE Trans Syst Man Cybern Part C (Appl Rev) 33(1):56–66

    Article  Google Scholar 

  • Fraser NM, Hipel KW (1979) Solving complex conflicts. IEEE Trans Syst Man Cybern 9(12):805–816

    Article  Google Scholar 

  • Gai T, Cao M, Chiclana F, Zhang Z, Dong Y, Herrera-Viedma E, Wu J (2023) Consensus-trust driven bidirectional feedback mechanism for improving consensus in social network large-group decision making. Group Decis Negot 32(1):45–74

    Article  Google Scholar 

  • Gong Z, Xu C, Chiclana F, Xu X (2017) Consensus measure with multi-stage fluctuation utility based on china’s urban demolition negotiation. Group Decis Negot 26:379–407

    Article  Google Scholar 

  • Han X, Nguyen Dieu Linh T, Xu H (2013) Conflict analysis based on the graph model for conflict resolution and grey matrix. Grey Syst Theory Appl 3(1):95–106

    Article  Google Scholar 

  • Han X, Dleu T, Nguyen L, Xu H (2013) Conflict analysis based on rough set in e-commerce. Int J Adv Manage Sci 2(1):1–8

    Google Scholar 

  • Howard N (1971) Paradoxes of rationality: theory of metagames and political behavior, vol 1. MIT Press, Cambridge

    Google Scholar 

  • Howard N (1994) Drama theory and its relation to game theory. part 1: Dramatic resolution vs. rational solution. Group Decis Negotiat 3:187–206

    Article  Google Scholar 

  • Howard N (1994) Drama theory and its relation to game theory. Part 2: formal model of the resolution process. Group Decis Negot 3:207–235

    Article  Google Scholar 

  • Kilgour DM, Hipel KW, Fang L (1987) The graph model for conflicts. Automatica 23(1):41–55

    Article  Google Scholar 

  • Kuang H, Bashar MA, Hipel KW, Kilgour DM (2015) Grey-based preference in a graph model for conflict resolution with multiple decision makers. IEEE Trans Syst Man Cybern Syst 45(9):1254–1267

    Article  Google Scholar 

  • Kuang H, Hipel KW, Kilgourt DM, Bashar MA (2013) A case study of grey-based preference in a graph model for conflict resolution with two decision makers. In: 2013 IEEE international conference on systems, man, and cybernetics, pp 2037–2041 IEEE

  • Li KW, Hipel KW, Kilgour DM, Fang L (2004) Preference uncertainty in the graph model for conflict resolution. IEEE Trans Syst Man Cybern Part A Syst Hum 34(4):507–520

    Article  Google Scholar 

  • Li Y, Kou G, Li G, Peng Y (2022) Consensus reaching process in large-scale group decision making based on bounded confidence and social network. Eur J Oper Res 303(2):790–802

    Article  Google Scholar 

  • Liu S, Dang Y, Fang Z (2021) Grey systems: theory and its applications. Science Press, Beijing

    Google Scholar 

  • Liu S, Yang Y, Xie N, Forrest J (2016) New progress of grey system theory in the new millennium. Grey Syst Theory Appl 6(1):2–31

    Article  Google Scholar 

  • Nash J (1950) Equilibrium points in n-person games. Proc Nat Acad Sci 36(1):48–49

    Article  Google Scholar 

  • Nash J (1951) Non-cooperative games. Ann Math 54(2):286–295

    Article  Google Scholar 

  • Rêgo LC, Vieira GIA (2017) Symmetric sequential stability in the graph model for conflict resolution with multiple decision makers. Group Decis Negot 26:775–792

    Article  Google Scholar 

  • Sina Financial (2022). The 126 million ecological compensation for gambling in shandong and henan has been settled, and the compensation amount is difficult to cover the investment. In Chinese. Accessed: 2023-03-17. https://finance.sina.com.cn/china/gncj/2022-07-10/doc-imizmscv0926527.shtml

  • Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Priceton University Press, New Jersey

    Google Scholar 

  • Wu N, Kilgour DM, Hipel KW, Xu Y (2021) Matrix representation of stability definitions for the graph model for conflict resolution with reciprocal preference relations. Fuzzy Sets Syst 409:32–54

    Article  Google Scholar 

  • Wu N, Xu Y, Hipel KW (2019) The graph model for conflict resolution with incomplete fuzzy reciprocal preference relations. Fuzzy Sets Syst 377:52–70

    Article  Google Scholar 

  • Wu N, Xu Y, Kilgour DM, Fang L (2020) Composite decision makers in the graph model for conflict resolution: Hesitant fuzzy preference modeling. IEEE Trans Syst Man Cybern Syst 51(12):7889–7902

    Article  Google Scholar 

  • Wu N, Xu Y, Wang H, Kilgour DM (2023) Matrix representation and behavioral analysis in a graph model for conflict resolution with incomplete fuzzy preferences. IEEE Trans Syst Man Cybern Syst

  • Xinhua Net Henan Channel (2022) Review of ecological protection and high-quality development in the yellow river basin in henan. In Chinese. Accessd: 2023-03-17. http://ha.news.cn/news/2022-05/17/c_1128656063.htm

  • Xu H, Hipel KW, Kilgour DM, Fang L (2018) Conflict resolution using the graph model: strategic interactions in competition and cooperation, vol 153. Springer, Berlin

    Book  Google Scholar 

  • Xu H, Zhao J, Ke GY, Ali S (2019) Matrix representation of consensus and dissent stabilities in the graph model for conflict resolution. Discrete Appl Math 259:205–217

    Article  Google Scholar 

  • Xu W, Chen X, Dong Y, Chiclana F (2021) Impact of decision rules and non-cooperative behaviors on minimum consensus cost in group decision making. Group Decis Negot 30:1239–1260

    Article  Google Scholar 

  • Yu J, Hipel KW, Kilgour DM, Fang L (2017) Fuzzy strength of preference in the graph model for conflict resolution with two decision makers. In: 2017 IEEE international conference on systems, man, and cybernetics (SMC), pp 3574–3577. IEEE

  • Yu J, Hipel KW, Kilgour DM, Fang L (2019) Fuzzy levels of preference strength in a graph model with multiple decision makers. Fuzzy Sets Syst 377:71–84

    Article  Google Scholar 

  • Zhang B, Dong Y, Herrera-Viedma E (2019) Group decision making with heterogeneous preference structures: an automatic mechanism to support consensus reaching. Group Decis Negot 28:585–617

    Article  Google Scholar 

  • Zhang C, Zhao M, Zhao L, Yuan Q (2021) A consensus model for large-scale group decision-making based on the trust relationship considering leadership behaviors and non-cooperative behaviors. Group Decis Negot 30:553–586

    Article  Google Scholar 

  • Zhao S, Xu H, Zhu J (2018) Conflict analysis graph model based on consensus preference of decision makers. Control Decis 33(8):1497–1504

    Google Scholar 

  • Zhao Y, Gong Z, Wei G, Słowiński R (2023) Consensus modeling with interactive utility and partial preorder of decision-makers, involving fairness and tolerant behavior. Inf Sci 638:118933

    Article  Google Scholar 

  • Zhu Q, Sarkis J, Geng Y (2011) Barriers to environmentally-friendly clothing production among Chinese apparel companies. Asian Bus Manage 10:425–452

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC) (71971115, 72201126, 72001096), Key Laboratory of Intelligent Decision and Digital Operations, Ministry of Industrial and Information Technology (NJ2023027), Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX23_0406), and a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (RGPIN-2015-04013, RGPIN-2022-03514).

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Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 211106, Jiangsu, Nanjing, People’s Republic of China

    Jinmuzi Zhang & Haiyan Xu

  2. Faculty of Business Administration, Memorial University of Newfoundland, St. John’s, NL, A1B 3X5, Canada

    Ginger Y. Ke

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  1. Jinmuzi Zhang
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  2. Haiyan Xu
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Correspondence to Haiyan Xu.

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Zhang, J., Xu, H. & Ke, G.Y. A Novel Consensus and Dissent Framework Under Grey Preference Based on the Graph Model for Conflict Resolution for Two Decision Makers. Group Decis Negot (2024). https://doi.org/10.1007/s10726-024-09882-0

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