Can Entropy Weight Method Correctly Reflect the Distinction of Water Quality Indices?

Entropy weight method (EWM) is a widely used weighting approach in water quality evaluation that assigns weights according to the discriminating degree of indicators. A higher discrete degree corresponds to a larger weight requirement, and vice versa. By using two water quality evaluation examples, this study proves that the weighting result of EWM cannot accurately reflect the information content and discriminability of indices in many conditions. For the EWM that uses the directly generating quotient (DGQ) in standardization, when the concentration dataset contains many zero values, the EWM results become prone to distortion. Similarly, for the EWM that utilizes the generating quotient after range pretreatment (GQARP) in standardization, when similar maximum values are present in the concentration dataset, the EWM results become prone to distortion. From the distortion weighting results of EWM, those indicators with high pollution degrees can be easily neglected, thereby leading to overoptimistic comprehensive water quality evaluation results. Although the source of distortion in the EWM results can be traced to the standardization and ranging processes, a solution to this problem is not yet available. In sum, the conventional EWM cannot correctly reflect the distinction of water quality indices; and it cannot be directly applied in water quality evaluation.