Stochastic Local Mutation for Efficient Membership Function Exploration in Fuzzy Classifiers

In fuzzy systems such as Learning Fuzzy-Classifier Systems (LFCSs), an appropriate design of membership functions (MFs), such as bell-shaped or triangular ones, is crucial for achieving high performance. However, determining suitable MFs for unknown tasks remains challenging, which often requires trial-and-error approaches. Recently, an LFCS with Self-Adaptive Membership (AFCS) has been proposed to address this issue by automatically adapting MF types during learning. Nevertheless, increasing the variety of adaptable MF types expands the search space, which may degrade learning performance. To overcome this challenge, we propose a stochastic local mutation operator that models and exploits the probability distribution of MFs from promising rules. The proposed operator performs local exploration around beneficial MF structures while maintaining global exploration capability through random mutation. We evaluate our approach using 25 classification problems, comparing seven methods including neural networks and different LFCS variants. Experimental results demonstrate that AFCS with the proposed operator, which adaptively combines local and global exploration strategies, improves both learning speed and final classification accuracy, demonstrating statistically significant superiority over all tested methods. These findings suggest that the proposed mutation operator effectively addresses the challenges posed by increased MF types while maintaining the advantages of adaptive MF selection in AFCS.