An Entropy-Based Approach to Fuzzy Multi-objective Optimization of Reservoir Water Quality Monitoring Networks Considering Uncertainties

In this study, a new fuzzy methodology for a multi-objective optimization of reservoir Water Quality Monitoring Stations (WQMS) was developed, based on Transinformation Entropy (TE), the IRanian Water Quality Index (IRWQI), and fuzzy social choice considering uncertainties. The approach was utilized in the Karkheh Dam reservoir in Iran. The objective functions were: 1) minimizing costs, 2) minimizing redundant information and uncertainties, and 3) maximizing the spatial coverage of the network. A CE-QUAL-W2 model was used for the simulation of water quality variables. The IRWQI was computed to reveal a complete picture of the reservoir water quality. The TE quantities were calculated for each pair of potential stations. The TE values were plotted against the spatial distances among potential WQMS to obtain the TE–Distance (TE–D) curve, and minimize redundant information among stations, while providing coverage of the entire network. A multi-objective Genetic Algorithm (NSGA-II) was applied to obtain Pareto-optimal solutions taking stakeholder preference into account. The most preferred solution was then obtained using fuzzy social choice approaches to achieve a consensus. The fuzziness embedded in the decision-making procedure, the uncertainty in the value of mutual information, and the uncertainty in identifying the optimal distance among WQMS were also investigated. Results indicated that the three fuzzy social choice approaches (Borda Count, Minimax, and Approval Voting) led to the same number of optimized WQMS in each fuzzy alpha-cut. Based on the fuzzy linguistic quantifiers method, the number of optimized WQMS was increased.