A Novel Non-Iterative Parameter Estimation Method for Interval Type-2 Fuzzy Neural Networks Based on a Dynamic Cost Function

Non-iterative methods for parameter estimation for interval type-2 neuro-fuzzy structure are fast to implement, when compared to online methods, and need no –or a few– parameters to be tuned. In this paper, a novel dynamic cost function, which defines a relationship between the current and past errors, is defined. The minimization of the aforementioned cost function results in a decreasing sequence of error which makes the proposed method numerically more stable when compared to least squares-based methods. It is a well-known phenomenon that a matrix inversion may cause problems if the matrix to be inverted is ill-defined i.e. its condition number is far bigger than one. The use of a dynamic relationship between the current and past error adds more degrees of freedom which makes it possible to improve the condition number of the matrix. Comprehensive simulation studies are presented for the prediction of financial data sets. The simulation results shows the superior numerical stability of the proposed method as the mean value of the condition number is smaller. This finding results in more accurate matrix inversion to be done in the two-step matrix inversion.