Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systems

Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs). 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 has a generalization bias to produce as many crisp rules as possible. Experimental results on real-world classification tasks show that our LCS significantly outperformed LCSs with popular rule representations in test classification accuracy on up to 17 of the 25 datasets tested.