Identification of fuzzy neural networks by forward recursive input-output clustering and accurate similarity analysis

Abstract

The first phase is the system identification which includes a novel forward recursive input-output clustering (FRIOC) method for the structure initialization and the gradient descent algorithm for the parameter initialization. (2) The second phase is the system simplification which includes the accurate similarity analysis and merging method for similar fuzzy rules and the gradient descent algorithm for the parameter finalization. Parameter initialisation by gradient descent algorithm Similarity calculation No Similarity based merger Yes Similarity matrix Structure initialisation by forward recursive inputoutput clustering approach Structure simplification by similarity based merger method Parameter finalization by gradient descent algorithm t S S  max Structure simplification by identifying and removing redundant rules Initial Mamdani fuzzy neural network The final Mamdani fuzzy neural network

A Self-Evolving Fuzzy System Which Learns Dynamic Threshold Parameter by Itself

“…Therefore, the commonly used approach is to use the piecewise linear approximation of the Gaussian membership function, and two typical examples to make this approximation are to use triangle [37] or trapezoidal [34] membership functions. There are a small number of researches in recent years, for instance, [38], attempted to compute the intersection and union of the fuzzy sets using Gaussian membership function directly, without making any approximations in advance. However, this method is computationally expensive, and under the risk of the curse of dimensionality.…”