Fuzzy levels of preference strength in a graph model with multiple decision makers

Abstract

A new hybrid preference structure combining multiple-level strength of preference and fuzzy preference is proposed to facilitate the modeling and analysis of strategic conflicts involving multiple decision makers (DMs) with complex preferences using the Graph Model for Conflict Resolution (GMCR). The new preference structure, named fuzzy strength of preference, provides a more comprehensive and flexible representation of DMs' relative preferences among states. A key contribution of this paper is to redefine four graph model stability definitions for fuzzy preferences, fuzzy Nash stability (FNash), fuzzy general metarationality (FGMR), fuzzy symmetric metarationality (FSMR), and fuzzy sequential stability (FSEQ), as general stabilities, strong stabilities, and weak stabilities at each level, permitting deeper analysis of graph models with the new preference structure. The resulting methodology can be utilized to model and analyze complex multiple-DM conflicts, thereby enhancing the capability of the graph model to provide strategic insights. A graph model of the Zhanghe River water allocation conflict in China demonstrates that the method can find the evolution path of a conflict and give new strategic insights for both practitioners and researchers. The fuzzy strength of preference framework makes GMCR more capable for addressing a wider range of practical conflicts.