Fuzzy Systems Based On Center Of Gravity And Fuzzy Inference Modeling Method

The traditional modeling methods include mechanism modeling method, system identification modeling method, and fuzzy reasoning modeling method, etc. This paper adopts a new fuzzy reasoning modeling method for DISO system, i.e. the fuzzy transformation is introduced, and then based on the SISO center of gravity fuzzy system, constructing DISO fuzzy system by fuzzy transformation. Main contents are as follows:First of all, it introduces the fuzzy system, describes the development of fuzzy system, proposes the difficulty of constructing the DISO center of gravity fuzzy system, and gives the implications of this paper.Secondly, it gives the SISO center of gravity fuzzy system, DISO center of gravity fuzzy system and their corresponding probability distributions, the results show that the center of gravity fuzzy systems are regression functions; their digital characteristics meet the certain laws. Two DISO fuzzy systems are constructed respectively from the SISO center of gravity fuzzy systems based on circle operator of Goguen implication and Mamdani implication operator by fuzzy transformation. Compared with the center of gravity fuzzy system, the tedious process of computing is eliminated in these two fuzzy systems. The proof and simulate results show that the fuzzy systems based on fuzzy transformation have universal approximation and high approximate accuracy.Thirdly, using the fuzzy systems based on fuzzy transformation, both time-varying and time-invariant free movement models of second-order can be expressed as nonlinear differential equations of second-order with variable coefficients. It's a new method to realize the mathematical model with the form of differential equation. In order to be applied to reasoning the state of system conveniently, these two free movement models are expressed as the state space models respectively.Finally, using the linear edge, differential equation model of the time-invariant system based on circle operator of Goguen implication is transformed to linear differential equation model, and the simulate results show that the linear model still has high approximate accuracy.