Approximation of stochastic processes by T–S fuzzy systems

Abstract

Fuzzy systems can provide us with universal approximation models of deterministic input–output relationships, but in the stochastic environment few achievements related to the subject have so far achieved. In the paper a novel stochastic Takagi–Sugeno (T–S) fuzzy system is introduced to represent approximately existing randomness in many real-world systems. By recapitulating the general architecture of the stochastic T–S fuzzy rule-based system, we analyze systematically approximating capability of the stochastic system to a class of stochastic processes. By the canonical representation of the stochastic processes, the stochastic fuzzy system is capable of with arbitrary accuracy providing the approximation to the stochastic processes in mean square sense. Finally, an efficient algorithm for the stochastic T–S fuzzy system is developed. A simulation example demonstrates how a stochastic T–S fuzzy system can be constructed to realize the given stochastic process, approximately.