The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function of $\mathbb{R}$ , some equivalent conditions are obtained, with wh...The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function of $\mathbb{R}$ , some equivalent conditions are obtained, with which continuous fuzzy functions can be approximated to any degree of accuracy by the four-layer feedforward regular fuzzy neural networks $\sum\limits_{k = 1}^q {\tilde W_k } \cdot \left( {\sum\limits_{j = 1}^p {\tilde V_{kj} \cdot \sigma (\tilde X \cdot \tilde U_j + \tilde \Theta _j )} } \right)$ . Finally a few examples of such fuzzy functions are given.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19601012).
文摘The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function of $\mathbb{R}$ , some equivalent conditions are obtained, with which continuous fuzzy functions can be approximated to any degree of accuracy by the four-layer feedforward regular fuzzy neural networks $\sum\limits_{k = 1}^q {\tilde W_k } \cdot \left( {\sum\limits_{j = 1}^p {\tilde V_{kj} \cdot \sigma (\tilde X \cdot \tilde U_j + \tilde \Theta _j )} } \right)$ . Finally a few examples of such fuzzy functions are given.
