Basic Algorithms for EFS

Abstract

This chapter deals with fundamental algorithms for updating some parameters and statistical values as used in several evolving fuzzy systems approaches, demonstrated in the next chapter. These algorithms include update mechanisms for several important statistical values such as mean, variance, covariance etc. (Section 2.1) and a recursive incremental adaptation of linear consequent parameters in TS(K) fuzzy systems, also applicable to linear weights in neuro-fuzzy type systems. Hereby, we describe two different learning schemes, global learning (Section 2.2) and local learning (Section 2.3), provide an analytical and empirical comparison of these two approaches (Section 2.4) and also demonstrate why an adaptation of linear consequent (weight) parameters alone may not sufficiently perform if the behavior of the non-linear process changes (Section 2.5). We also outline some enhanced aspects and alternatives for adapting consequent parameters (Section 2.6) and will describe ways on how to incrementally learn non-linear antecedent parameters (Section 2.7). The chapter is concluded by discussing (the necessity of) possible alternatives for optimization functions based on which recursive (incremental) learning of antecedent and consequent parameters are carried out (Section 2.8).