This paper provides a sufficient criterion guaranteeing the robust global exponential stability (RGES) of fuzzy neural networks (FNN) with bis-disturbances, i.e., derivative contraction coefficients and piecewise constant arguments. By using the generalized Gronwall inequality and modular inequality, the upper bound of bis-disturbances is derived by solving the binary implicit transcendental equation as well as external spontaneous constraints respectively, ensuring the primitive stable FNN can be stable again in the presence of external bis-disturbances. Furthermore, the feasible boundary derived from the established criterion can guarantee that the mutual restraint and dynamic interconnection effects between the bis-disturbances that allow the system to be stable again can occur instead of being independent. Finally, the validity of the derived theoretical results is verified by simulation.