Skip to main content
SpringerLink
Log in

Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives

  • Living reference work entry
  • First Online:
Handbook of Group Decision and Negotiation

  • 183 Accesses

Abstract

Major extensions of the Graph Model for Conflict Resolution (GMCR) are delineated and illustrated. The matrix formulation allows stability calculations to be carried out more efficiently and provides a solid foundation for constructing theoretical advances. Simple (crisp) preferences can be extended for handling not only unknown preferences but also other kinds of uncertain preferences, such as fuzzy, grey, and probabilistic. In this chapter, we focus on fuzzy preferences and how they can be analyzed using the matrix method. Another recent extension of the graph model is to frame it within two systems perspectives, especially the inverse perspective, in which desirable outcomes and stability types are inputs whereas preferences to achieve them are outputs. These extensions increase the capability of the graph model to generate useful strategic advice and insights. A real-world water export conflict is used to illustrate these ideas.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Aljefri YM, Hipel KW, Fang L (2018) General hypergame analysis within the graph model for conflict resolution. Int J Syst Sci Oper Logist. https://doi.org/10.1080/23302674.2018.1476604

  • Bashar MA, Kilgour DM, Hipel KW (2012) Fuzzy preferences in the graph model for conflict resolution. IEEE T Fuzzy Syst 20(4):760–770

    Article  Google Scholar 

  • Bashar MA, Kilgour DM, Hipel KW (2014) Fuzzy option prioritization for the graph model for conflict resolution. Fuzzy Sets Syst 26:34–48

    Article  Google Scholar 

  • Bernath Walker SG, Hipel KW, Inohara T (2009) Strategic decision making for improved environmental security: coalitions and attitudes in the graph model for conflict resolution. J Syst Sci Syst Eng 18(4):461–476

    Article  Google Scholar 

  • Fang L, Hipel KW, Kilgour DM (1993) Interactive decision making: the graph model for conflict resolution. Wiley, New York

    Google Scholar 

  • Fang L, Hipel KW, Wang L (2002) Gisborne water export conflict study. In: Schmitz GH (ed) Proceedings of 3rd International conference on water resources and environment research (ICWRER), vol 1, Dresden, pp 432–436

    Google Scholar 

  • Fang L, Hipel KW, Kilgour DM, Peng X (2003a) A decision support system for interactive decision making, part 1: 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 (2003b) A decision support system for interactive decision making, part 2: analysis and output interpretation. IEEE T Syst Man Cybern Part C-Appl Rev 33(1):56–66

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fraser NM, Hipel KW (1988) Decision support systems for conflict analysis. In: Proceedings of the IMACS/IFOR first international colloquium on managerial decision support systems and knowledge-based systems, Amsterdam, pp 13–21

    Google Scholar 

  • Garcia A, Hipel KW (2017) Inverse engineering preferences in simple games. Appl Math Comput 311:184–194

    Google Scholar 

  • Hamouda L, Kilgour DM, Hipel KW (2004) Strength of preference in the graph model for conflict resolution. Group Decis Negot 13:449–462

    Article  Google Scholar 

  • Hamouda L, Kilgour DM, Hipel KW (2006) Strength of preference in graph models for multiple decision-maker conflicts. Appl Math Comput 179(1):314–327

    Google Scholar 

  • He S, Kilgour DM, Hipel KW (2017) A general hierarchical graph model for conflict resolution with application to greenhouse gas emission disputes between USA and China. Eur J Oper Res 257(3):919–932

    Article  Google Scholar 

  • Hipel KW, Kilgour DM, Fang L, Peng X (1997) The decision support system GMCR in environmental conflict management. Appl Math Comput 83(2–3):117–152

    Google Scholar 

  • Hipel KW, Fang L, Kilgour DM (2008) Decision support systems in water resources and environmental management. J Hydrol Eng 13(9):761–770

    Article  Google Scholar 

  • Hipel KW, Sakamoto M, Hagihara Y (2015) Third party intervention in conflict resolution: dispute between Bangladesh and India over control of the Ganges river. In: Hagihara K, Asahi C (eds) Coping with regional vulnerability: preventing and mitigating damages from environmental disasters. Springer, Tokyo, pp 329–355

    Google Scholar 

  • Hipel KW, Fang L, Kilgour DM (2019) The graph model for conflict resolution: reflections on three decades of development. Group Decis Negot: https://doi.org/10.1007/s10726-019-09648-z

  • Inohara T, Hipel KW, Bernath Walker SG (2007) Conflict analysis approaches for investigating attitudes and misperceptions in the war of 1812. J Syst Sci Syst Eng 16(2):181–201

    Article  Google Scholar 

  • Inohara T, Hipel KW (2008a) Coalition analysis in the graph model for conflict resolution. Syst Eng 11(4):343–359

    Article  Google Scholar 

  • Inohara T, Hipel KW (2008b) Interrelationships among noncooperative and coalition stability concepts. J Syst Sci Syst Eng 17(1):1–29

    Article  Google Scholar 

  • Kilgour DM, Hipel KW, Fang L, Peng X (2001) Coalition analysis in group decision support. Group Decis Negot 10(2):159–175

    Article  Google Scholar 

  • Kinsara RA, Kilgour DM, Hipel KW (2015a) Inverse approach to the graph model for conflict resolution. IEEE Trans Syst Man Cybern-Syst 45(5):734–742

    Article  Google Scholar 

  • Kinsara RA, Petersons O, Hipel KW, Kilgour DM (2015b) Advanced decision support system for the graph model for conflict resolution. J Decis Syst 24(2):117–145

    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 

  • 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 KW, Kilgour DM, Hipel KW (2005) Status quo analysis in the graph model for conflict resolution. J Oper Res Soc 56:699–707

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Obeidi A, Hipel KW, Kilgour DM (2005) The role of emotions in envisioning outcomes in conflict analysis. Group Decis Negot 14(6):481–500

    Article  Google Scholar 

  • Peng X, Hipel KW, Kilgour DM, Fang L (1997) Representing ordinal preferences in the decision support system GMCR II. In: Proceedings of 1997 IEEE international conference syst man and cybernetics, Florida, pp 809–814

    Google Scholar 

  • Rêgo LC, dos Santos AM (2015) Probabilistic preferences in the graph model for conflict resolution. IEEE Trans Syst Man Cybern-Syst 45(4):595–608

    Article  Google Scholar 

  • Wang M, Hipel KW, Fraser NM (1988) Modelling misperceptions in games. Behav Sci 33(3):207–223

    Article  Google Scholar 

  • Wang M, Hipel KW, Fraser NM (1989) Solution concepts in hypergames. Appl Math Comput 34(3):147–171

    Google Scholar 

  • Wang J, Hipel KW, Fang L, Xu H, Kilgour DM (2017) Behavioural analysis in the graph model for conflict resolution. IEEE Trans Syst Man Cybern-Systems 49:904. https://doi.org/10.1109/TSMC.2017.2689004

    Article  Google Scholar 

  • Wang J, Hipel KW, Fang L, Dang Y (2018) Matrix representations of the inverse problem in the graph model for conflict resolution. Eur J Oper Res 270(1):282–293

    Article  Google Scholar 

  • Xu H, Hipel KW, Kilgour DM (2009) Matrix representation of solution concepts in multiple decision maker graph models. IEEE Trans Syst Man Cybern Part A-Syst Hum 39(1):96–108

    Article  Google Scholar 

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

    Book  Google Scholar 

  • Yu J, Kilgour DM, Hipel KW, Zhao M (2015) Power asymmetry in conflict resolution with application to a water pollution dispute in China. Water Resour Res 51(10):8627–8645

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zhu Z, Kilgour DM, Hipel KW (2018) A new approach to coalition analysis within the graph model. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2018.2811402

Download references

Author information

Authors and Affiliations

  1. Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada

    Keith W. Hipel & Yi Xiao

  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    D. Marc Kilgour

  3. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Haiyan Xu

Authors
  1. Keith W. Hipel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Marc Kilgour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haiyan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yi Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Keith W. Hipel .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University Dept. Mathematics, Waterloo, ON, Canada

    D. Marc Kilgour

  2. University of Strathclyde Strathclyde Business School, Glasgow, UK

    Colin Eden

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Hipel, K.W., Kilgour, D.M., Xu, H., Xiao, Y. (2020). Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives. In: Kilgour, D., Eden, C. (eds) Handbook of Group Decision and Negotiation. Springer, Cham. https://doi.org/10.1007/978-3-030-12051-1_45-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-12051-1_45-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12051-1

  • Online ISBN: 978-3-030-12051-1

  • eBook Packages: Springer Reference Behavioral Science and PsychologyReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences

Publish with us

Policies and ethics

Search

Navigation