Interpolation Functions Of General Type-2 Fuzzy Systems

This paper focuses on simplifying the use procedure and calculation of general type-2 fuzzy systems by way of extracting their the interpolation functions. Firstly, four kinds of fuzzification methods with special laws are designed to construct the general type-2 fuzzy sets in the antecedents and consequents of type-2 inference rules. On this basis, together with the KM algorithm, alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-plane representation and interpolation conclusions of interval type-2 fuzzy systems, three types of interpolation functions of general type-2 fuzzy systems are obtained. In the meantime, all of the interpolation functions have been proved as universal approximators. It can be seen that in future applications of general type-2 fuzzy systems, interpolation functions can be applied directly instead of conventional blocks. Because of the ingenious design of the general type-2 fuzzy sets on operations, the computation of general type-2 fuzzy systems has been greatly reduced. In order to verify the validity and superiority of the proposed methods, simulation results with a type-1 fuzzy system, an interval type-2 fuzzy system and two general type-2 fuzzy systems for the approximation problem of dynamic systems are presented. The simulations exhibit that the suggested approaches have good and desired performance.