Preference uncertainty in the graph model for conflict resolution

A new preference structure is introduced into the graph model for conflict resolution. This structure can handle a decision-maker's (DM) strict preference for one state or scenario over another, equal preference for states, and uncertain or unknown preference in the comparison of two states. Built upon this preference structure, four types of solution definitions modeling human behavior under conflict are extended to accommodate uncertainty in preferences. Four distinct ways to consider uncertain preference information are identified, producing sixteen extended stability definitions. Interrelationships of these definitions within and across the four definition sets are investigated. Illustrative examples of two-DM and multi-DM conflict models are presented to show how the new solution concepts can be applied in practice.