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Interval fuzzy preferences in the graph model for conflict resolution

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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.

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Acknowledgements

The authors appreciate receiving helpful advice from anonymous referees which improved the quality of their paper. They also would like to express their appreciation to Prof. Ni-Bin Chang of the University of Central Florida for suggesting that they incorporate interval fuzzy preference into the GMCR methodology. The first author is grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support from NSERC Discovery grants.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Jeddah, Dhahban, 23881, Saudi Arabia

    M. Abul Bashar

  2. Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    M. Abul Bashar, Keith W. Hipel, D. Marc Kilgour & Amer Obeidi

  3. Centre for International Governance Innovation, Waterloo, ON, N2L 6C2, Canada

    Keith W. Hipel

  4. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    D. Marc Kilgour

  5. Department of Management Sciences, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Amer Obeidi

Authors
  1. M. Abul Bashar
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  2. Keith W. Hipel
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  3. D. Marc Kilgour
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  4. Amer Obeidi
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Correspondence to M. Abul Bashar.

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Bashar, M.A., Hipel, K.W., Kilgour, D.M. et al. Interval fuzzy preferences in the graph model for conflict resolution. Fuzzy Optim Decis Making 17, 287–315 (2018). https://doi.org/10.1007/s10700-017-9279-7

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  • DOI: https://doi.org/10.1007/s10700-017-9279-7

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