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Interval fuzzy preferences in the graph model for conflict resolution

Author

Listed:
  • M. Abul Bashar

    (University of Jeddah
    University of Waterloo)

  • Keith W. Hipel

    (University of Waterloo
    Centre for International Governance Innovation)

  • D. Marc Kilgour

    (University of Waterloo
    Wilfrid Laurier University)

  • Amer Obeidi

    (University of Waterloo
    University of Waterloo)

Abstract

A new analysis technique, appropriate to situations of high preference uncertainty, is added to the graph model for conflict resolution methodology. Interval fuzzy stabilities are now formulated, based on decision makers’ (DMs’) interval fuzzy preferences over feasible scenarios or states in a conflict. Interval fuzzy stability notions enhance the applicability of the graph model, and generalize its crisp and fuzzy preference-based stability ideas. A graph model is both a formal representation and an analysis procedure for multiple participant-multiple objective decisions that employs stability concepts representing various forms of human behavior under conflict. Defined based on a type-2 fuzzy logic, an interval fuzzy preference for one state over another is represented by a subinterval of [0, 1] indicating an interval-valued preference degree for the first state over the second. The interval fuzzy stabilities put forward in this research are interval fuzzy Nash stability, interval fuzzy general metarational stability, interval fuzzy symmetric metarational stability, and interval fuzzy sequential stability. A state is interval fuzzy stable for a DM if moving to any other state is not adequately desirable to the DM; where adequacy is measured by the interval fuzzy satisficing threshold of the DM and farsightedness, involving possible moves and countermoves by DMs, is determined by the interval fuzzy stability notion selected. Note that infinitely many degrees in an interval-valued preference are preserved in characterizing the desirability of a move. A state from which no DM can move to any sufficiently desirable scenario is an interval fuzzy equilibrium, and is interpreted as a possible resolution of the strategic conflict under study. The new stability concept is illustrated through its application to an environmental conflict that took place in Elmira, Ontario, Canada. Insightful results are identified and discussed.

Suggested Citation

  • M. Abul Bashar & Keith W. Hipel & D. Marc Kilgour & Amer Obeidi, 2018. "Interval fuzzy preferences in the graph model for conflict resolution," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 287-315, September.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9279-7
    DOI: 10.1007/s10700-017-9279-7
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    References listed on IDEAS

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    1. Keith W. Hipel & Amer Obeidi, 2005. "Trade versus the environment: Strategic settlement from a systems engineering perspective," Systems Engineering, John Wiley & Sons, vol. 8(3), pages 211-233, September.
    2. K W Li & D M Kilgour & K W Hipel, 2005. "Status quo analysis in the graph model for conflict resolution," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 699-707, June.
    3. D. Marc Kilgour & Keith W. Hipel, 2005. "Introduction to the Special Issue on the Graph Model for Conflict Resolution," Group Decision and Negotiation, Springer, vol. 14(6), pages 439-440, November.
    4. D. Marc Kilgour & Keith W. Hipel, 2005. "The Graph Model for Conflict Resolution: Past, Present, and Future," Group Decision and Negotiation, Springer, vol. 14(6), pages 441-460, November.
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    Cited by:

    1. Shinan Zhao & Haiyan Xu, 2019. "A Novel Preference Elicitation Technique Based on a Graph Model and Its Application to a Brownfield Redevelopment Conflict in China," IJERPH, MDPI, vol. 16(21), pages 1-14, October.
    2. Zhao, Shinan & Xu, Haiyan & Hipel, Keith W. & Fang, Liping, 2019. "Mixed stabilities for analyzing opponents’ heterogeneous behavior within the graph model for conflict resolution," European Journal of Operational Research, Elsevier, vol. 277(2), pages 621-632.
    3. Jing Yu & Ling-Ling Pei, 2018. "Investigation of a Brownfield Conflict Considering the Strength of Preferences," IJERPH, MDPI, vol. 15(2), pages 1-11, February.
    4. Shawei He, 2019. "Coalition Analysis in Basic Hierarchical Graph Model for Conflict Resolution with Application to Climate Change Governance Disputes," Group Decision and Negotiation, Springer, vol. 28(5), pages 879-906, October.
    5. Liangyan Tao & Xuebi Su & Saad Ahmed Javed, 2021. "Inverse Preference Optimization in the Graph Model for Conflict Resolution based on the Genetic Algorithm," Group Decision and Negotiation, Springer, vol. 30(5), pages 1085-1112, October.
    6. Huang, Yuming & Ge, Bingfeng & Hipel, Keith W. & Fang, Liping & Zhao, Bin & Yang, Kewei, 2023. "Solving the inverse graph model for conflict resolution using a hybrid metaheuristic algorithm," European Journal of Operational Research, Elsevier, vol. 305(2), pages 806-819.
    7. Ming Tang & Huchang Liao, 2022. "A graph model for conflict resolution with inconsistent preferences among large-scale participants," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 455-478, September.
    8. Keith W. Hipel & Liping Fang & D. Marc Kilgour, 2020. "The Graph Model for Conflict Resolution: Reflections on Three Decades of Development," Group Decision and Negotiation, Springer, vol. 29(1), pages 11-60, February.

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