Determining a network size for a fuzzy neural network structure is very important, and it is often difficult to obtain the most suitable value. This study develops a self-evolving function-link interval type-2 fuzzy neural network (SEFT2FNN) that autonomously constructs the rule base with the initial empty and the membership functions. The function-link is applied to an interval type-2 fuzzy neural network to give a more accurate approximation of the function. The adaptive laws for the proposed system are derived using the steepest descent gradient approach. The stability of system was guaranteed using Lyapunov function approach. Finally, the performance of the proposed system is verified using the numerical simulations of the nonlinear system identification and the control of time-varying plants. (c) 2017 Elsevier B.V. All rights reserved.