An Improved Entropy Weight Method Mitigating Grade Distortion in Water Quality Assessment

The Entropy Weight Method (EWM) is a prevalent and objective technique for assigning weights in water quality assessment. However, engineering practice has shown that distortion phenomena occur in water quality assessment results based on the EWM. This study reveals EWM’s distortion in grade discrimination via theory and case studies. To address this, we developed an improved entropy weight model (I-EWM) based on fuzzy variable set theory, which determines weights by incorporating both pollution degree and grade discrimination capacity. We quantify an indicator’s grade discrimination level and pollution degree using the fuzzy entropy and first-order moment of its average membership vector, respectively. A specific water quality assessment example was used to demonstrate the effectiveness of the I-EWM. The I-EWM significantly altered the weight allocation: the weights for CODMn, NH3-N, and TP shifted from (0.687, 0.185, 0.127) to (0.191, 0.428, 0.381). When applied to the five monitoring points, the I-EWM produced markedly different results from the EWM. The water quality grades shifted from a pattern of (“Good”, “Good”, “Good”, “Good”, “Medium”) to a more conservative and realistic assessment of (“Medium”, “Medium”, “Poor”, “Poor”, “Poor”). Theoretical analysis demonstrates that the I-EWM provides more reasonable water quality assessments and effectively addresses the grade discrimination distortion inherent in the EWM.