Fuzzy self-organizing map

Abstract

Kohonen's Self-Organizing Map is one of the best-known neural network models. In this paper, we introduce a fuzzy version of the model called: Fuzzy Self-Organizing Map. We replace the neurons of the original model by fuzzy rules, which are composed of fuzzy sets. The fuzzy sets define an area in the input space, where each fuzzy rule fires. The output of each rule is a singleton. The outputs are combined together by a weighted average, where the firing strengths of the fuzzy rules act as the weights. The weighted average gives a continuous valued output for the system. Thus the Fuzzy Self-Organizing Map performs a mapping from a n-dimensional input space to one-dimensional output space. The learning capability of the Fuzzy Self-Organizing Map enables it to model a continuous valued function to an arbitrary accuracy. The learning is done by first self-organizing the centers of the fuzzy sets according to Kohonen's Self-Organizing Map learning laws. After that, the fuzzy sets and the outputs of the fuzzy rules are initialized. Finally, in the last phase of the new learning method, the fuzzy sets are tuned by an algorithm similar to Kohonen's Learning Vector Quantization 2.1. Simulation results of a two-dimensional sinc function show good accuracy and fast convergence.