A novel neural network (NN)-based nonlinear decentralized adaptive controller is proposed for a class of large-scale, uncertain, interconnected nonlinear systems in strict-feedback form by using the dynamic surface control (DSC) principle, thus, the "explosion of complexity" problem which is observed in the conventional backstepping approach is relaxed in both state and output feedback control designs. The matching condition is not assumed when considering the interconnection terms. Then, NNs are utilized to approximate the uncertainties in both subsystem and interconnected terms. By using novel NN weight update laws with quadratic error terms as well as proposed control inputs, it is demonstrated using Lyapunov stability that the system states errors converge to zero asymptotically with both state and output feedback controllers, even in the presence of NN approximation errors in contrast with the uniform ultimate boundedness result, which is common in the literature with NN-based DSC and backstepping schemes. Simulation results show the effectiveness of the approach.