Modeling linguistic intuitionistic fuzzy preference into the consensus and dissent framework of graph model for conflict resolution and its application

The intensification of water scarcity and pollution has elevated the strategic significance of cross-border water resources. Their transnational nature complicates ownership and use rights, leading to conflicts. The graph model for conflict resolution (GMCR) has proven effective in addressing strategic disputes. However, decision-makers' preferences, influenced by a complex interplay of cultural, economic, and political factors, are too intricate to quantify precisely in cross-border water resource conflicts. Besides, despite the importance of consensus being widely researched in the group decision-making field, its study within GMCR remains limited. To address these challenges, we develop a new consensus and dissent framework of GMCR with linguistic intuitionistic fuzzy preference relations (LIFPRs). As a qualitative tool, LIFPRs composed of linguistic intuitionistic fuzzy numbers (LIFNs) can capture DMs' certainty, uncertainty, and hesitation. Specifically, we first propose a score function of LIFNs and some necessary definitions to model LIFPRs into GMCR. Then, we study the consensus and dissent framework of GMCR with LIFPRs in logical form. Additionally, we provide the corresponding matrix representation for future decision support system development. This study is applied to the Mekong River conflict, suggesting that the Mekong River Commission and China should engage in a comprehensive cooperative negotiation process.