A fuzzy system describes hunman language information by fuzzy rules

it is an important tool to deal with the uncertain information.Mamdani fuzzy system and Takagi-Sugeno (T-S) fuzzy system are two kinds of common systems.Firstly

the two types of systems are unified by introducing a control parameter so as to establish a generalized hybrid fuzzy system in this paper.Secondly

the hybrid fuzzy system can approximate to a continuous differentiable function with respect to infinite norm through Taylor formula with Peano remainder term of multivariate function

and certify that this system also has the second order approximation accuracy by means of Hessian matrix in Lagrange remainder term.Finally

the results show that the approximation effect of the hybrid fuzzy system based on the modeling of control parameters is better than the separate Mamdani or T-S fuzzy system by choosing sample points analysis.