Function approximation through fuzzy systems using taylor series expansion-based rules: Interpretability and parameter tuning

Abstract

In this paper we present a new approach for the problem of approximating a function from a training set of I/O points using fuzzy logic and fuzzy systems. Such approach, as we will see, will provide us a number of advantages comparing to other more-limited systems. Among these advantages, we may highlight the considerable reduction in the number of rules needed to model the underlined function of this set of data and, from other point of view, the possibility of bringing interpretation to the rules of the system obtained, using the Taylor Series concept. This work is reinforced by an algorithm able to obtain the pseudooptimal polynomial consequents of the rules. Finally the performance of our approach and that of the associated algorithm are shown through a significant example.