Sufficient condition of universal approximation of fuzzy controllers with generalized linear membership function

A new kind of generalized linear membership function (abbr. GLMF) is designed in the paper, and triangle or trapezoid membership function, used widely in theory and application of fuzzy controllers, can be as its´ special cases. Based on the derivation of analytical structure of mamdani fuzzy controllers with GLMF, the sufficient condition for the fuzzy controllers as an universal approximator is given by method of the linear interpolation. On the condition of the same approximation error, less number of input fuzzy sets are required to approximate any given continuous function for fuzzy controllers with GLMF, than that with triangle or trapezoid membership function. Finally, some simulation are given to manifest the effect of the design.