Universal approximation of T-S fuzzy systems

The relationship between the approximation accuracy and the membership functions, the defuzzifier and number of fuzzy rule of T-S fuzzy systems are studied. According to mathematical properties of continuous function, the universal approximation properties of fuzzy mapping in only one interval are analyzed, and some related theorems are proposed and proved. Then, the sufficient conditions of the general T-S fuzzy systems with universal approximation are derived from these theorems, which helps establish the new relationship between approximation error bounds and the number of the fuzzy rules of different T-S fuzzy systems. Finally, the paper proposes some suggestions to construct T-S fuzz systems with universal approximation.