Matrix representation of the graph model for conflict resolution based on intuitionistic preferences with applications to trans-regional water resource conflicts in the Lancang–Mekong River Basin

With the continual growth in global demand for water resources, the governance of trans-regional water resources has become an important field of cooperation between countries, and conflicts caused by competition for water resources have become a focal issue in international relations. The root causes of trans-regional water resource conflicts include unclear ownership of water resources and the limited rationality of the parties involved. The water rights trading model has proven to play a stabilizing role in resolving trans-regional water resource conflicts versus the traditional negotiation model. To demonstrate the rationality and theoretical strength of the water rights trading model in allocating trans-regional water resources in uncertain environments, this paper proposes a novel matrix representation of intuitionistic stability definitions through a graph model for conflict resolution (GMCR). First, decision-makers’ (DMs’) intuitionistic preferences, unilateral movements, and intuitionistic unilateral improvements in a GMCR with two DMs are represented in a matrix. The joint unilateral movements and joint intuitionistic unilateral improvements for a coalition in a GMCR with multiple DMs are also represented. Next, according to the logical forms of intuitionistic stability definitions, four stability definitions in a GMCR with intuitionistic preferences were redefined to enable matrix representations of graph models with either two DMs or multiple DMs. Finally, we analyzed the state transitions and strategies of all stakeholders in trans-regional water resource conflicts in the Lancang-Mekong River Basin within the intuitionistic graph model. The contributions of this paper are twofold. First, in terms of theoretical research, this article enriches and develops the GMCR and proposes a set of definitions of matrix intuitionistic stability. Second, in terms of practical application, the intuitionistic stability analysis results can provide a reference for water rights trading to solve trans-regional water resource conflicts in uncertain environments and transform trans-regional water resource governance systems.