SIRMs Fuzzy Inference Model with Linear Transformation of Input Variables and Universal Approximation

Abstract

The automatic construction of fuzzy system with a large number of input variables involves many difficulties such as large time complexity and getting stuck in a shallow and local minimum. As models to overcome them, the SIRMs (Single Input Rule Modules) and DIRMs (Double Input Rule Modules) models have been proposed. However, they are not always effective in accuracy. In the previous paper, we have proposed the model composed of two phases; the first is a linear transformation of input to intermediate variables and the second is to use SIRMs model. It was shown that the proposed model is superior in accuracy and the number of rules to the conventional models in numerical simulation. In this paper, we will show theoretically that the proposed model is a universal approximator. Further, in order to show the effectiveness of the proposed model, numerical simulation will be performed.