Fuzzy Pattern Trees for Classification Problems Using Genetic Programming

Fuzzy Pattern Trees (FPTs) are tree-based structures in which the internal nodes are fuzzy operators, and the leaves are fuzzy features. This work uses Genetic Programming (GP) to evolve FPTs and assesses their performance on 20 benchmark classification problems. The results show improved accuracy for most of the problems in comparison with previous works using different approaches. Furthermore, we experiment using Lexicase Selection with FPTs and demonstrate that selection methods based on aggregate fitness, such as Tournament Selection, produce more accurate models before analysing why this is the case. We also propose new parsimony pressure methods embedded in Lexicase Selection, and analyse their ability to reduce the size of the solutions. The results show that for most problems, at least one method could reduce the size significantly while keeping a similar accuracy. We also introduce a new fuzzification scheme for categorical features with too many categories by using target encoding followed by the same scheme for numerical features, which is straightforward to implement, and avoids a much higher increase in the number of fuzzy features.