Matrix Representation and Behavioral Analysis in a Graph Model for Conflict Resolution With Incomplete Fuzzy Preferences
研究了在多个决策者具有不完全模糊偏好关系的图模型中，用矩阵方法识别稳定状态，并将四种不完全模糊偏好关系与五种经典稳定性定义结合，得到二十种稳定性定义的矩阵表示，通过行为分析判断哪些定义与期望均衡一致。
A solution concept (or stability definition) determines whether a state is stable for a decision-maker (DM) in a Graph Model for Conflict Resolution. An equilibrium according to that stability definition is a state stable for all DMs. Thus, stability definitions correspond to anticipated patterns of collective behavior in conflicts. This study focuses on a matrix method to identify stable states in a graph model with multiple DMs whose preferences are fuzzy relations, possibly incomplete. The four distinct approaches to incomplete fuzzy preference relations (IFPRs) are integrated with five classical stability definitions to produce matrix representations of twenty incomplete fuzzy stability definitions. Behavioral analysis and knowledge of DMs’ IFPRs can then be applied to identify which stability definitions are consistent with desired equilibrium states. Matrix representations and behavior analysis are illustrated using a model of a real-world conflict—a demolition dispute in Jiangsu Province, China.