Water Quality Index (WQI) Forecasting and Analysis Based on Neuro-Fuzzy and Statistical Methods

Water quality is crucial to the economy and ecology because a healthy aquatic eco-system supports human survival and biodiversity. We have developed the Neuro-Adapt Fuzzy Strategist (NAFS) to improve water quality index (WQI) forecasting accuracy. The objective of the developed model is to achieve a balance by improving prediction accuracy while preserving high interpretability and computational efficiency. Neural networks and fuzzy logic improve the NAFS model’s flexibility and prediction accuracy, while its optimized backward pass improves training convergence speed and parameter update effectiveness, contributing to better learning performance. The normalized and partial derivative computations are refined to improve the model. NAFS is compared with ANN, Adaptive Neuro-Fuzzy Inference System (ANFIS), and current machine learning (ML) models such as LSTM, GRU, and Transformer based on performance evaluation metrics. NAFS outperforms ANFIS and ANN, with MSE of 1.678. NAFS predicts water quality better than ANFIS and ANN, with RMSE of 1.295. NAFS captures complicated water quality parameter interdependencies better than ANN and ANFIS using principal component analysis (PCA) and Pearson correlation. The performance comparison shows that NAFS outperforms all baseline models with the lowest MAE, MSE, RMSE and MAPE, and the highest R2, confirming its superior accuracy. PCA is employed to reduce data dimensionality and identify the most influential water quality parameters. It reveals that two principal components account for 72% of the total variance, highlighting key contributors to WQI and supporting feature prioritization in the NAFS model. The Breusch–Pagan test reveals heteroscedasticity in residuals, justifying the use of non-linear models over linear methods. The Shapiro–Wilk test indicates non-normality in residuals. This shows that the NAFS model can handle complex, non-linear environmental variables better than previous water quality prediction research. NAFS not only can predict water quality index values but also enhance WQI estimation.