A new fuzzy approach and bankruptcy theory in risk estimation in Waste Load Allocation

Abstract

In this paper, we developed a simulator-optimizer model based on risk analysis to determine Waste Load Allocation (WLA). A new Fuzzy index as Fuzzy Risk Index (FRI) was linked with multi-objective optimization to minimize FRI for the environmental stakeholder and the total cost of sewage treatment for the polluting industries as the other collective stakeholder. Afterwards, the conflict was resolved with the help of Nash bargaining and bankruptcy approach (Constrained Equal Awards Rule). The model was run using quantitative/qualitative data for the KhoramAbad River. To check the efficiency of FRI, the process followed for WLA was reimplemented by the Monte Carlo simulation (MCS). A comparison between the two approaches revealed that the outcomes derived from Fuzzy arithmetic across all aspects, encompassing river qualitative simulation, nondominated curve, Nash bargaining's agreed point, and bankruptcy output, closely mirrored the results of MCS. The notable distinction lies in the drastic reduction of the model's execution time by a factor of 450.

Keywords: Bankruptcy theory; Fuzzy Risk Index (FRI); KhoramAbad River; Monte Carlo Simulation (MCS); Nondominated Sorting Genetic Algorithm (NSGA-II); Waste Load Allocation (WLA).