Learning evolving Mamdani fuzzy systems based on parameter optimization

Evolving fuzzy systems are widely recognized to be able to capture the non-stationary phenomenon of data stream. Most existing algorithms for the parameter identification problem of evolving fuzzy systems are built on heuristic methods rather than the optimal method, when there is a structure change of the system such as rule adding, merging or removing. In order to address this issue, this paper proposes a new online learning algorithm with time varying structure and parameters from a parameter optimization point of view, in which the influence between fuzzy rules is naturally considered, to identify evolving Mamdani fuzzy systems. Firstly, to minimize the local error function and get the accurate (rather than heuristic) weighted recursive least square estimation of the consequent parameters, the methods for structure changing and parameter updating are obtained. Further, these methods are proved leading to a new effective algorithm for optimum solutions. Moreover, for the proposed online learning approach, a special type of weighted recursive least square updating formulas of the consequent parameters are proposed. Numerical experiments and comparisons with other state-of-art algorithms demonstrate that the proposed algorithm can achieve better predictions than other algorithms judged by accuracy.