An approach to the functions approximation problems by Mamdani fuzzy system

In this paper, we introduce a class of piecewise multilinear models for Mamdani fuzzy system and investigate their approximation capabilities to integrable functions with L
^p
-norm. Specially, by extending fuzzy system to stochastic one, the approximation capability of the stochastic Mamdani system to a class of random processes is analyzed. A result on the approximation of regular function is given showing that fuzzy system may keep their semantic structure while approximating to any degree of accuracy not only sufficiently regular functions, but also their derivatives.