An inexact optimization approach for river water-quality management

Area of Science:

• Environmental Science
• Water Resource Management
• Systems Engineering

Background:

• Existing fuzzy waste load allocation models (FWLAM) struggle with uncertainty in defining membership functions for pollution control agencies (PCA) and dischargers.
• Grey systems theory offers a framework to handle imprecise or incomplete information, which is common in environmental management.

Purpose of the Study:

• To extend a previously developed FWLAM by incorporating grey systems to address uncertainty in membership function parameters.
• To provide flexibility for both the PCA and dischargers to independently define their goals using interval grey numbers.
• To develop a grey fuzzy optimization model that balances decision-making latitude with system uncertainty reduction.

Main Methods:

• The study extends a fuzzy waste load allocation model (FWLAM) by integrating grey systems theory.
• A multiobjective optimization framework is employed, treating membership function parameters as interval grey numbers.
• The concept of an acceptability index is utilized to derive a deterministic equivalent of the grey fuzzy optimization model.

Main Results:

• The enhanced grey fuzzy waste load allocation model (GFWLAM) demonstrates improved optimal solutions compared to previous models.
• The model successfully maximizes the width of interval-valued fractional removal levels, allowing for greater decision-making flexibility.
• It also minimizes the width of the goal fulfillment level, effectively reducing system uncertainty.

Conclusions:

• The integration of grey systems theory significantly enhances the robustness of fuzzy waste load allocation models.
• The developed GFWLAM provides a more flexible and less uncertain approach to river pollution management.
• The methodology offers a valuable tool for environmental agencies in optimizing pollution control strategies.