Intuitionistic fuzzy strength preference in the graph model considering internal and external consensus

Twelve years after the Fukushima nuclear accident, the Fukushima Daiichi Nuclear Power Plant (FDNPP) officially began discharging nuclear wastewater into the ocean on August 24, 2023. As the wastewater contains radioactive substances, its discharge is expected to damage both local and global marine ecosystems, triggering strong opposition from the public and neighboring countries. With rising global uncertainty, the nuclear wastewater discharge, as a conflict under complex environmental conditions, requires preference structures that account for two essential characteristics of human decision-making-intuitionism and strength differentiation. Based on this, a new preference structure, the intuitionistic fuzzy strength preference (IFSP), is constructed within the graph model for conflict resolution (GMCR) framework. Considering that the effective resolution of conflict events often depends not only on individual preferences but also on the degree of coordination within decision-making groups and consensus among different groups (two essentially different but coexisting forms of consensus), this study proposes the concepts of internal consensus and external consensus, along with corresponding consensus computation methods. On this basis, a new set of stability definitions is introduced in the GMCR framework based on the IFSP and internal-external consensus, in order to derive feasible solutions to the conflict. The developed model is then applied to the Fukushima nuclear wastewater discharge conflict. The stability analysis reveals four equilibria, among which s 7 is identified as the most stable and likely outcome. In s 7 , Japan discharges the wastewater without technological improvement, while neighboring countries impose sanctions and international organizations exercise supervision and condemnation. This equilibrium underscores the effectiveness of a combined pressure mechanism. The analysis further elucidates why alternative states are less sustainable: for instance, the absence of international oversight ( s 5 ) or sanctions ( s 10 ) fails to exert sufficient pressure on Japan, whereas an overly confrontational approach ( s 11 ) risks escalating the conflict.