Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At f...Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.展开更多
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This work was supported by National Natural Science Foundation(699740 4 1 699740 0 6)
文摘Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.
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.
