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Fuzzy strength of preference in the Graph Model for Conflict Resolution with two decision makers

A new hybrid preference framework of the Graph Model for Conflict Resolution (GMCR) is proposed to facilitate modeling and analysis of conflicts involving two decision makers (DMs) with fuzzy levels of preference. The new preference structure, a hybrid of models of three-level strength of preference and fuzzy preference, provides a more flexible technique to express DMs' relative preferences among states, and is more comprehensive and flexible than existing models. One key contribution of this paper is to extend four graph model stability definitions for fuzzy preferences, consisting of fuzzy Nash stability (FR), fuzzy general metarationality (FGMR), fuzzy symmetric metarationality (FSMR), and fuzzy sequential stability (FSEQ), to the new hybrid preference structure. This extension permits the analysis of the hybrid model, including both strong and weak stabilities. The resulting modeling and analysis system can be applied to complex two-decision-maker conflicts, thereby enhancing the ability of the graph model to provide strategic insights. A specific two decision-maker conflict is utilized to illustrate the practical application of the new hybrid preference framework for GMCR.