Fuzzy preferences in a two-decision maker graph model

A fuzzy preference framework is developed within the paradigm of the graph model for conflict resolution. This framework takes into account both certain and uncertain information about the preferences of decision makers (DMs) involved in a strategic conflict. The graph model is a solution methodology for conflict decision making that begins with a model of the problem and suggests possible resolutions through a number of stability definitions. Four basic fuzzy stability definitions are introduced for a two-DM graph model to analyze conflict behavior and identify possible resolutions even when preferences are fuzzy. Fuzzy stability definitions describe varied human behavior in a conflict model; a state is fuzzy stable for a DM according to a specific fuzzy stability definition if a move to any other state, evaluated according to that definition, does not meet the DM´s fuzzy satisficing threshold. A state that is fuzzy stable for all DMs under a specific fuzzy stability definition constitutes a fuzzy equilibrium under that definition, and is interpreted as a possible resolution of the conflict. Fuzzy stability definitions include fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability.