An algebraic approach to conflict resolution with hybrid preference in two decision maker graph models

An algebraic approach is proposed to calculate stabilities in two decision maker graph models with combining preference. The algebraic approach establishes a hybrid framework for stability analysis by combining strength and uncertainty for Preference. The hybrid system is more general than existing models, which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, the matrix representations of Nash and sequential stabilities are defined and algorithms are developed to calculate efficiently the essential inputs of the stabilities. A specific case study, including two decision makers and hybrid preference, is carried out to illustrate how the proposed method can be applied in practice.