Analyses for Lp(?)-norm approximation capability of generalized Mamdani fuzzy systems ?
The connected piecewise linear functions are introduced to study the Lp(?)-norm approximation capability of the generalized Mamdani fuzzy system. It is shown that such general fuzzy systems are the universal approximators to the p-integrable functions with Lp(?)-norm. For the given degree of accuracy an upper bound of the fuzzy rule numbers needed in the fuzzy rule base of the system is estimated. Finally a simulation example is analyzed to demonstrate our conclusions.
generalized mamdani fuzzy system connected piecewise linear function universal approximation