A Linguistic Preference Framework for the Graph Model for Conflict Resolution with Application to Water Resource Disputes

When stakeholders conflict over shared water resources, identifying solutions they can realistically accept is a long-standing challenge in decision analysis. This paper develops a new Graph Model for Conflict Resolution (GMCR) that allows decision-makers to express their preferences using natural language, including nuanced hedged terms such as “more or less” and “roughly”, making conflict analysis more consistent with how stakeholders actually reason in practice.

Our key contributions are:

• A linguistic preference framework for representing qualitative and uncertain judgements within GMCR.
• Four new stability definitions tailored to linguistic preference scenarios.
• An application to a water rights conflict in China’s Yellow River Basin, producing more realistic equilibrium outcomes than existing crisp and fuzzy GMCR variants.

This work bridges qualitative human reasoning with formal conflict analysis, offering practitioners a more faithful tool for mediating real-world disputes over shared resources.

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