Multiobjective Evolutionary Optimization for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a 'one pass' manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimize the training error of the models on historical training data or alternatively to iteratively minimize the intracluster variance of the clusters obtained via online data partitioning. This recognizes the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimizing the training error may potentially lead to overfitting while minimizing the intracluster variance does not necessarily ensure the optimized prototype-based models to attain improved classification outcomes. To achieve better classification performance while avoiding overfitting for zero-order EISs, this article presents a novel multiobjective optimization approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final nondominated set of the resulting optimized models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimization approach in improving the classification performance of zero-order EISs.