Graph Model for Conflict Resolution with Grey Information and Application

The preferences of (Decision makers)DMs may be uncertain as a result of much more uncertain information existing such as grey information, in real conflict problems, so that it is difficult for the classical graph model for conflict resolution(GMCR) to make quantitatively the preference ranking and deal with. In view of this, the grey number is introduced to express grey information, and then a ranking method is proposed to determine the grey preference rankings of DMs, so that a novel graph model with grey information is established to solve equilibrium states and decision paths. By means of analyzing a conflict example, the results show that the proposed model can deal with conflict problems with uncertain information well, and objectively give the preference rankings of conflict states of decision makers in the form of a quantitative description instead of subjective judgment.