Local Optimality of Self-Organising Neuro-Fuzzy Inference Systems

Optimality of the premise, IF part is critical to a zero-order evolving intelligent system (EIS) because this part determines the validity of the learning results and overall system performance. Nonetheless, a systematic analysis of optimality has not been done yet in the state-of-the-art works. In this paper, we use the recently introduced self-organising neuro-fuzzy inference system (SONFIS) as an example of typical zero-order EISs and analyse the local optimality of its solutions. The optimality problem is firstly formulated in a mathematical form, and detailed optimality analysis is conducted. The conclusion is that SONFIS does not generate a locally optimal solution in its original form. Then, an optimisation method is proposed for SONFIS, which helps the system to attain local optimality in a few iterations using historical data. Numerical examples presented in this paper demonstrate the validity of the optimality analysis and the effectiveness of the proposed optimisation method. In addition, it is further verified numerically that the proposed concept and general principles can be applied to other types of zero-order EISs with similar operating mechanisms.