Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs), a family of rule-based machine learning systems that evolve interpretable models through evolutionary processes. However, it is very difficult to choose an appropriate rule representation for each problem. Additionally, some problems benefit from using different representations for different subspaces within the input space. Thus, an adaptive mechanism is needed to choose an appropriate rule representation for each rule in LCSs. This article introduces a flexible rule representation using a four-parameter beta distribution and integrates it into a fuzzy-style LCS. The four-parameter beta distribution can form various function shapes, and this flexibility enables our LCS to automatically select appropriate representations for different subspaces. Our rule representation can represent crisp/fuzzy decision boundaries in various boundary shapes, such as rectangles and bells, by controlling four parameters, compared to the standard representations such as trapezoidal ones. Leveraging this flexibility, our LCS is designed to adapt the appropriate rule representation for each subspace. Moreover, our LCS incorporates a generalization bias favoring crisp rules where feasible, enhancing model interpretability without compromising accuracy. Experimental results on real-world classification tasks show that our LCS achieves significantly superior test accuracy and produces more compact rule sets. Our implementation is available at https://github.com/YNU-NakataLab/Beta4-UCS. An extended abstract related to this work is available at https://doi.org/10.36227/techrxiv.174900805.59801248/v1.

翻译：规则表示对学习分类器系统（LCS）这一族通过进化过程演化可解释模型的基于规则的机器学习系统的搜索能力与决策边界具有重要影响。然而，为每个问题选择合适的规则表示十分困难。此外，某些问题受益于在输入空间的不同子空间中使用不同的表示形式。因此，需要一种自适应机制来为LCS中的每条规则选择合适的规则表示。本文提出了一种使用四参数Beta分布的灵活规则表示，并将其集成到模糊风格LCS中。四参数Beta分布能够形成多种函数形状，这种灵活性使得我们的LCS能够为不同子空间自动选择合适的表示。与梯形等标准表示相比，我们的规则表示通过控制四个参数，能够以矩形、钟形等多种边界形状表示清晰/模糊的决策边界。利用这种灵活性，我们的LCS被设计为能为每个子空间自适应地选择合适的规则表示。此外，我们的LCS引入了在可行情况下倾向于清晰规则的泛化偏置，从而在不牺牲准确性的前提下增强了模型的可解释性。在真实世界分类任务上的实验结果表明，我们的LCS取得了显著更优的测试准确率，并生成了更紧凑的规则集。我们的实现可在 https://github.com/YNU-NakataLab/Beta4-UCS 获取。与本工作相关的扩展摘要可在 https://doi.org/10.36227/techrxiv.174900805.59801248/v1 查阅。