A novel integration of regret-based methodology and bankruptcy theory for waste load allocation

Abstract

This article proposes a novel approach to tackle the ambiguity and limitation of the Fuzzy Risk Index in assessing the severity of river pollution based on a regret theory named River Quality Regret Index (RQRI). RQRI and total treatment cost respectively represent the conflicting objectives of environmental protection and pollutant management within the river-pollutant system. Using a multi-objective optimizer simulator model, Nash bargaining identifies the agreement from the non-dominant solutions found on the exchange curve of these objectives.To further account for the spatial distribution of pollutant discharge, a new framework, Namin rule, is developed by integrating RQRI with the bankruptcy approach for waste load allocation.Implementation of this methodology on the KhoramAbad River using quantitative and qualitative data reveals the efficacy of RQRI compared to the Fuzzy risk, particularly when pollutant sources are dispersed. Additionally, Namin rule, compared to the constrained equal awards rule, demonstrates a greater utilization of the river's self-purification capacity in such scenarios. This framework offers a robust and flexible tool for managing river pollution by balancing environmental and economic considerations.