Center of gravity fuzzy system based on regular fuzzy implication and it's probability representation

In this paper, we consider a fundamental theoretical question: why cannot regular fuzzy implication operator meeting logical properties construct fuzzy system? Through the appropriate choice of the aggregation operator, the center of gravity fuzzy system (COGFS) based on regular fuzzy implication is studied in detail in the paper. Numerical characteristics of the random vector corresponding to the above system have more normative format. Which is important to do the further research on unified theory of uncertain systems. Finally, we also discuss the universal approximation of the system. It proves that the system has higher approximation accuracy for nonlinear function, and the simulation result also illustrates the effective of conclusion.

I. Introduction

In 1973, Zadeh proposed the compositional rules of inference approach (CRI) [2], and then it was extensively applied to fuzzy control. Over the past few decades, the study of fuzzy system and fuzzy control have attracted the interests of many experts and scholars. Wang first proved the approximation of fuzzy systems by Stone-Weierstranss theorem [3], in which it showed fuzzy systems were capable of approximating any real continuous function on a compact set to arbitrary accuracy. Subsequently, universal approximation of different forms of fuzzy systems were also studied in the papers [4], [5]. All these provided a theoretical basis for the design of fuzzy system and fuzzy controller.