Inverse Preference Optimization in the Graph Model for Conflict Resolution with Uncertain Cost

When a conflict occurs, the disputants involved and interested third parties usually expect to reach the desired equilibrium. To achieve this goal, inverse graph model for conflict resolution is an effective way to make the state of interest an equilibrium by ascertaining the required preferences. However, specifying crisp cost or effort of changing preferences over states can be challenging for decision makers (DMs) and third parties. As a result, a new inverse preference optimization model using interval optimization is introduced into the graph model by considering the uncertain cost of preference adjustment. First, the preference adjustment cost with uncertainty is formulated using interval number. Then, pessimistic preference ordering and DMs’ degrees of risk tolerance are utilized to compare cost intervals. After that, an inverse preference optimization model with uncertain adjustment cost is established. Finally, an illustrative example of the bulk water export conflict in Canada is presented to demonstrate the feasibility and effectiveness of the proposed approach.