An integrated algebraic approach to conflict resolution with three-level preference

An integrated algebraic approach is developed to calculate stabilities in multiple decision maker graph models with three levels of preference. The algebraic approach establishes an integrated paradigm for stability analysis and status quo analysis under different preference structures, such as two-level preference and three-level preference. Difficulties in coding algorithms to analyze stabilities, rooted in their logical representation, led to the development of matrix representations of preference and explicit matrix calculations to determine stabilities. Here, the algebraic approach is used to represent graph models with three levels of preference and to conduct stability analysis for such models. The algebraic approach facilitates the development of new stability concepts and algorithms to calculate them, and reveals an inherent link between status quo analysis and traditional stability analysis. Hence, it will facilitate the design of an integrated decision support system for the graph model for conflict resolution.