Learning evolving T-S fuzzy systems with both local and global accuracy – a local online optimization approach

Most real data streams are non-linear and non-stationary by nature, which makes it a challenging issue to develop effective learning techniques. With the advantages of updating the system structure and parameters on the fly, evolving fuzzy systems (EFSs) are effective paradigms to address this issue. However, existing methods and algorithms of EFSs are usually: (1) developed based on a heuristic rather than an optimal approach and put main focus on tracking the most recent local model, thus leading to an “unlearning effect” and often poor global accuracy; (2) lack of optimality of the consequent parameters when there is a structure update of the fuzzy system. In order to resolve these issues, this paper proposes a local error optimization approach (LEOA) for identifying evolving T-S fuzzy systems. LEOA has its antecedent learning method derived from minimizing a bunch of local error functions and guarantee the optimality of the consequent parameters by a new extended weighted recursive least square (EWRLS) method. Furthermore, mathematical proofs and calculations are provided to verify the optimality and ϵ-completeness property of LEOA. Numerical examples based on several benchmark and real-world data sets are tested, and the results demonstrate that LEOA not only makes preferable local prediction accuracy compared with existing state-of-the-art methods but also reserves the global accuracy of the identified models.