A granular computing view on function approximation

Abstract

This paper investigates function approximation problem from a granular computing point of view and proposes a new granular based approximation scheme. It is proved that the proposed scheme has the universal approximation property and then is generally applicable for wide applications. Compared with the widely used approximation schemes such as fuzzy systems and neural networks, the proposed approximation scheme has several interesting and useful features such as a global view to achieve the comprehensive understanding about the behaviors of functions or systems being approximated, as good interpretability and transparency as fuzzy systems but much more powerful in overcoming the curse of dimensionality, and much more flexible and effective in incremental learning. Index Terms—Granular computing, function approximation, interval analysis, fuzzy systems, neural networks.