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.