A New Fuzzy Approach and Bankruptcy Theory in Risk Estimation in Waste Load Allocation

Abstract

In this paper, a simulator-optimizer model based on risk analysis was developed to determine the 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). The comparison between the two approaches showed the results obtained from the Fuzzy arithmetic of all fields, including the river qualitative simulation, non-overlapping procedure, agreed point by Nash bargaining, and bankruptcy output, were very close to the results of the MCS.