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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 …