Viability of two adaptive fuzzy systems based on fuzzy c means and subtractive clustering methods for modeling Cadmium in groundwater resources

The Adaptive Neuro-Fuzzy Inference System (ANFIS) combines the strengths of both Artificial Neural Networks (ANNs) and Fuzzy Logic (FL) into a single framework. By doing so, it allows for quicker learning and adaptable interpretation capabilities, which are useful for modeling complex patterns and identifying nonlinear relationships. One significant challenge in assessing water quality is the difficulty and time-consuming nature of determining the various factors that impact it. Given this situation, predicting heavy metal levels in groundwater resources, both urban and rural, is essential. This paper investigates two methods, ANFIS-FCM and ANFIS-SUB, to determine their effectiveness in modeling Cadmium (Cd) in groundwater resources. ‏The parameters to be considered are: dissolved solids (TDS), electroconductivity (EC), turbidity (TU), and pH were assumed to be the independent variables. A total of 51 sampling location were used with in the groundwater resource were used to develop the fuzzy models. For evaluating the performance of ANFIS-FCM and ANFIS-SUB models, three different performance criteria including the correlation coefficient, root mean square error, and sum square error were used for comparing the model outputs with actual outputs‏.‏ Based on the obtained results from scatter plots of actual and predicted value by ANFIS-SUB and ANFIS- FCM models, the determination coefficient (R(2)) value for total data, test and train sets is equal to 0.978, 0.982, 0.993 and to 0.983, 0.999 and 0.998 respectively. This result proved the Cd predictions of the implemented ANFIS-FCM model was significantly close to the measured all experimental data with R(2) of 0.983. The performance of the implemented ANFIS-FCM model was compared with the ANFIS-SUB model and it is found that the ANFIS-FCM provided slightly higher accuracy than the ANFIS-SUB model. Also, the results obtained from the comparison between the predicted and the actual data indicated that the ANFIS-FCM and ANFIS-SUB have a strong potential in estimating the heavy metals in the groundwater with a high degree of accuracy.