Matrix representation of stability definitions in the graph model for conflict resolution with grey-based preferences

Abstract

Within the structure of the graph model for conflict resolution (GMCR), a new matrix representation approach is introduced to analyze the strategic conflicts with grey-based preferences for decision-makers (DMs). Specifically, the DM’s grey-based preferences, unilateral movements (UMs), and grey unilateral improvement (GUI) are redefined by the matrix representation. Furthermore, for the multiple DMs graph model, the joint UMs and joint GUIs for a collection of more than two DMs also have been represented by the matrix expression. Then, the matrix representation approach is used to describe and determine the stability of the given state for a focus DM based on different grey-based stability definitions, as well as, that also means the DM has different behavioral patterns in conflict when the DM has grey-based preferences. In summary, the matrix representation approach is proposed to determine and analyze individual stability and equilibrium for both two DM and multiple DMs graph models based on the framework of different grey stability definitions. Finally, a real application to a generic sustainable development conflict and Elmira groundwater contamination conflict is illustrated to show the usefulness and correctness of the matrix representation of GMCR with grey-based preferences.