Summary: If the transitive function \(\sigma:R\to R\) is a Tauber-Wiener function, i.e., the three-layer feedforward neural network \(\sum^n_{i=1}\nu_i\cdot \sigma(u_i\cdot x+\theta_i)\) is the universal approximator, we study in the paper the approximation representation of a class of fuzzy functions – continuous fuzzy closure mappings by the four-layer feedforward fuzzy neural network \(\sum^p_{k=1}\widetilde W_k\cdot\sum^q_{j=1}\widetilde V_{kj}\cdot\sigma(\widetilde U_j\cdot\widetilde X+\widetilde\Theta_j)\). Fuzzy closure mappings characterize the continuous fuzzy functions that can be arbitrarily closely approximated by the fuzzy neural network.