In this study, the structure of fuzzy functions is improved by function expansion. Unlike fuzzy conventional if-then rules, classical fuzzy function structure includes fuzzy bases and linear inputs. Membership functions of fuzzy bases are set using fuzzy C-means (FCM) algorithm, and the linear parameters are computed using the least-square estimation (LSE). This study has two main contributions. First, conventional "fuzzy functions" structure is powered by the expansion of orthogonal "trigonometric functions" where the approximation capabilities of the fuzzy functions are increased. Second, the widths of the normalized membership functions determined for the fuzzy function model are optimized using the Nelder-Mead simplex algorithm that provides further enhancement on the identification performance. The advantages of the proposed model are shown via offline identification of a benchmark nonlinear system and online identification of two real-time nonlinear systems.