Matrix Representation and Behavioral Analysis in a Graph Model for Conflict Resolution With Incomplete Fuzzy Preferences

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.