Impact of Variations in Membership Functions on the Performance of <scp>ANFIS</scp> for Nonlinear Systems as a Benchmark

Abstract

ABSTRACT The design of membership functions (MFs) has a significant effect on how well the ANFIS controller performs. This study methodically assesses the impact of MF variations on the control performance of nonlinear systems, utilizing the inverted pendulum as a reference point. Multiple ANFIS controllers are developed and trained using Gaussian, Triangular, Trapezoidal, and Generalized Bell‐shaped MFs. The models are assessed based on critical performance metrics, including rise time, settling time, overshoot, steady‐state error, and root mean square error (RMSE). The results demonstrate that Gaussian and Bell‐shaped MFs yield smoother control actions and faster convergence, whereas Triangular and Trapezoidal MFs provide lower computational complexity but exhibit reduced robustness. These findings highlight the importance of MF selection in optimizing ANFIS‐based control strategies for nonlinear dynamical systems.