A fuzzy multi-stakeholder socio-optimal model for water and waste load allocation

This study proposes a fuzzy multi-stakeholder socio-optimal methodology for joint water and waste load allocation (WWLA) in river systems while addressing upstream flow uncertainty and different social choice rules (SCRs). QUAL2Kw, as the numerical river water quality model, is executed for various scenarios of water and waste loads to construct a comprehensive dataset of plausible settings, which is in turn used to train a meta-model in the form of multivariate linear regressions. The river upstream flow as the main uncertain parameter is assessed by fuzzy transformation method (FTM). Then, for different confidence levels of fuzzy uncertain input, the meta-model is linked with the non-dominated sorting genetic algorithm (NSGA-II) multi-objective optimization model to generate trade-off curves among the stakeholders' utility functions. Subsequently, five SCRs are utilized at each confidence level to determine the fuzzy interval solutions for each objective. Next, the possibility degree method is applied to rank the fuzzy interval solutions in each α-cut level. Finally, considering the priorities of all stakeholders, the fallback bargaining method is used to specify the most appropriate SCR in each confidence level. Application of the proposed methodology in Kor River, Iran, shows its efficacy to realize the socio-optimal WWLA scenario(s) among different stakeholders.