ArticleScientific reports2026
Integrating Pythagorean fuzzy numbers into the graph model to resolve water resource conflicts in the Yellow River Basin.
Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Conflicts over sustainable water resource development trigger social unrest, constrain economic development, and exacerbate geopolitical tensions. The graph model for conflict resolution (GMCR) provides a feasible tool for resolving such disputes. However, the complex uncertainty of such conflicts makes it difficult for traditional GMCR to yield satisfactory solutions for each decision-maker (DM). In this paper, Pythagorean fuzzy numbers are incorporated into the graph model framework to express DMs’ true preferences. For the first time, a Pythagorean fuzzy graph model is proposed to solve complex real-world conflicts. A new preference-ranking method accounting for trust relationships supplements traditional GMCR to determine the true preferences of individual DMs with common interests (composite decision-makers). DM weights are calculated based on point degree centrality and proximity centrality. A group decision matrix is obtained using the Pythagorean fuzzy weighted average operator, and comprehensive scores are calculated using Romanian selection and the group score matrix to rank alternatives. On this basis, new stability definitions collectively called Pythagorean fuzzy stability are proposed in GMCR. Finally, the model is successfully applied to conflicts over sustainable water resource development in the Yellow River, expanding the theoretical scope of GMCR and providing feasible solutions for resolving water resource conflicts.
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