Analyze the effect of number of fuzzy rules on fuzzy model performance in simulating soil water movement

Fuzzy methods in simulating water flow in to the soil has attracted the attention of researchers because of the possibility of considering the uncertainty and variability of the parameters in this methods. The sensitivity of the fuzzy model is to find the balance between the accuracy of the fuzzy model and its speed of execution, which depends on the number of fuzzy rules. Therefore, our goal in this research is to investigate the effect of the number of fuzzy rules on the accuracy of the model. In order to achieve this, the fuzzy model for predicting water movement in unsaturated soil was evaluated by considering fuzzy sets with different supports and consequently different rule numbers. The rules of the fuzzy model were derived from the large training sets obtained by numerical solution of Richards equation by using HYDRUS-1D model. The results showed that increasing the number of fuzzy rules initially increased the accuracy of the model (NRMSE value decreased from 4.3 to 3.1 and maximum error value from 0.128 to 0.09 for fuzzy model with 9 and 49 rules, respectively but by increasing the number of input fuzzy sets and increasing the rules to 81, the accuracy of the fuzzy model was reduced. The reason for the reduced efficiency of the fuzzy model is rules overlap.