Interpolation functions of interval type-2 fuzzy systems

The interpolation functions of interval type-2 fuzzy systems and their universal approximation are investigated in this paper. Two types of fuzzification methods are designed to construct the antecedents and consequents of the type-2 inference rules. Then the properties of the fuzzy operator and the type-reduction algorithm are used to integrate all parts of the fuzzy system. Interpolation functions of interval type-2 fuzzy systems, which are proved to be universal approximators, are obtained based on three models, namely single input and single output, double inputs and single output, and multiple inputs and single output. The proposed approach is applied to approximate experiments of dynamic systems so as to evaluate the system performance. The system parameters are optimized by the QPSO algorithm. Experimental results for several data sets are given to show the approximation performances of the proposed interpolation functions are better than those of the interpolation function of the classical type-1 fuzzy system.