Abstract: This paper distills the commonness of triangular and trapezoid membership functions,and explicitly defines the generalized trapezoid-shaped(GTS) membership functions which use these membership functions as two special cases.The explicit analytical expressions for type Ⅰ and typeⅡ two-dimensional simplest Mamdani fuzzy controllers are derived,of which the input variables adopt GTS membership functions.Analytical structures of the fuzzy controllers are deeply investigated,and it is proved that these two types of fuzzy controllers are equivalent to the variable structure combinations of nonlinear(or linear) PI controller and nonlinear(or constant) variable control offsets.Moreover,these fuzzy controllers are monotonically increasing,continuous and bounded with regard to the correspon-ding universe.Simultaneously,the better universality of this type of fuzzy controller is revealed.