Institute of Mathematics, Vietnamese Academy of Science and Technology 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam Department of Basis Science, University of Transport and Communications, Hanoi, Vietnam, .
2000 Mathematics Subject Classification: 41A30, 65D15, 94D05, 60G35.
In practice, many I/O systems, including fuzzy systems, operate in the environment which is essentially stochastic. Fuzzy systems must be able to learn by experience from environment. This property can be considered as being closely related to the approximating capabilities of the systems. In this paper we introduce a class of stochastic fuzzy systems, in which spline functions of degree two are used as membership functions of input variables. Then, in mean square sense, we investigate the capabilities of these fuzzy systems to approximate given stochastic processes with arbitrary accuracy. Finally, a numerical example is employed to demonstrate our results.
Brownian motion, Spectral representation, Stochastic fuzzy system, Stochastic integral, Universal approximation
