Enhancing social acceptability and environmental sustainability of inter-basin water transfers through the integration of bankruptcy rules and the fuzzy nucleolus concept

Ensuring equitable water allocation in existing inter-basin transfer projects requires balancing competing stakeholder priorities, respecting physical infrastructure constraints, and integrating socioeconomic needs with environmental sustainability considerations. This paper introduces a new, comprehensive framework designed to meet these challenges. The approach applies modified bankruptcy methods to divide water among basins according to each stakeholder’s relative power and uses stability metrics to identify the most equitable allocation method. The resulting water rights are then processed through a fuzzy Nucleolus-based model that redistributes resources and benefits to maximize stakeholder satisfaction. To address uncertainties in profitability and coalition behavior, fuzzy logic is applied to estimate stakeholder gains and participation levels. This new approach allows participants to contribute resources partially rather than fully to joint efforts. In this cooperative framework, both coefficients and variables are represented as fuzzy values, resulting in profit allocations expressed as fuzzy numbers. A comparison between cooperative and non-cooperative scenarios shows that this model leads to fairer and more efficient benefit sharing, with stakeholders earning higher profits through collaboration than they would individually. The results of our case study indicate that the Proportional (P) method and the Adjusted Proportional (AP) method, by considering the stakeholders’ power, provide the most stable and acceptable water allocations among stakeholders, while the P method offers greater transparency and simplicity. Adopting this cooperative approach boosted collective benefits by up to 12% compared to non-cooperative scenarios, while also significantly reducing inequality in both water distribution and economic gains. Also, the proposed bankruptcy method in this study reduced interannual allocation fluctuations by approximately 10 percent compared to classical bankruptcy theory approaches. This adjustment ensures a more equitable water distribution during drought years.