Improving FBF neurofuzzy approximator by optimised input space covering

Abstract

Possible improvements to neurofuzzy nets based on the Mamdani model are discussed. A new algorithm using an optimised clustering technique is proposed and a comparative test presented. Introduction: A large number of neurofuzzy networks are based on the classical Mamdani model. Particularly interesting in this regard is the FBF (fuzzy basis function) approach (l). This inter- prets the net output as the expansion of the unknown mapping in a suitable basis of functions, which are related to rules extracted by numerical and linguistic data. Several alternatives are possible depending on the choice of the basic ingredients of the Mamdani model (fuzzy logic reasoning, membership functions, fuzzy opera- tions, type of fuzzificatioddefuzzification). Consequently, in spite of the widespread use of neurofuzzy nets in actual applications, there still exists the necessity for improving their performance. A clear example is presented in (2), where a simple modification of classical fuzzy logic reasoning is introduced by using a compensa- tory parameter, with the effect that the resulting mapping is signif- icantly improved. In this Letter, we focus our attention on FBF implementation. We show how optimised input space coverage is able to greatly improve net performance. We propose an efficient method for tai- loring the membership functions (MFs) of the rules, extracted from the numerical data. The method is based on an optimised clustering of data in the conjunct input-output space. Network architecture: The FBF net relies on the Mamdani model, which is based on IF-THEN rules where both the antecedent and the subsequent parts are fuzzy quantities. Suppose that N rules have been extracted from the available data; the ith rule has the following structure: