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This paper presents the performance evaluation of the recently developed Sequential Adaptive Fuzzy Inference System (SAFIS) algorithm for classification problems. In SAFIS the number of fuzzy rules can be automatically determined according to learning process and the parameters in fuzzy rules can be updated simultaneously. Earlier SAFIS has been evaluated only for function approximation problems. Improvements to SAFIS for enhancing its performance in both accuracy and speed are described in the paper and the resulting algorithm is referred to as Extended SAFIS (ESAFIS). In ESAFIS, the concept of the modified influence of a fuzzy rule is introduced for adding or removing the fuzzy rules. If the input data does not warrant adding of fuzzy rules, the parameters of the fuzzy rules are updated using a Recursive Least Square Error (RLSE) scheme. Empirical study of ESAFIS is executed based on several commonly used classification benchmark problems. The results indicate that the proposed ESAFIS produces higher classification accuracy with reduced computational complexity compared with original SAFIS and other algorithms, such as eTS (Angelov and Filev 2004), Simpl_eTS (Angelov and Filev 2005) and k-NN (Huang et al. 2006).

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.

Abstract-In this paper, a correntropy-based evolving fuzzy neural system (correntropy-EFNS) is proposed for approximation of nonlinear systems. Different from the commonly used meansquare error criterion, correntropy has a strong outliers rejection ability through capturing the higher moments of the error distribution. Considering the merits of correntropy, this paper brings contributions to build EFNS based on the correntropy concept to achieve a more stable evolution of the rule base and update of the rule parameters instead of the commonly used meansquare error criterion. The correntropy-EFNS (CEFNS) begins with an empty rule base and all rules are evolved online based on the correntropy criterion. The consequent part parameters are tuned based on the maximum correntropy criterion where the correntropy is used as the cost function so as to improve the nonGaussian noise rejection ability. The steady-state convergence performance of the CEFNS is studied through the calculation of the steady-state excess mean square error (EMSE) in two cases: i) Gaussian noise; and ii) non-Gaussian noise. Finally, the CEFNS is validated through a benchmark system identification problem, a Mackey-Glass time series prediction problem as well as five other real-world benchmark regression problems under both noise-free and noisy conditions. Compared with other evolving fuzzy neural systems, the simulation results show that the proposed CEFNS produces better approximation accuracy using the least number of rules and training time and also owns superior non-Gaussian noise handling capability.