Genetically optimized fuzzy decision trees

In this study, we are concerned with genetically optimized fuzzy decision trees (G-DTs). Decision trees are fundamental architectures of machine learning, pattern recognition, and system modeling. Starting with the generic decision tree with discrete or interval-valued attributes, we develop its fuzzy set-based generalization. In this generalized structure we admit the values of the attributes that are represented by some membership functions. Such fuzzy decision trees are constructed in the setting of genetic optimization. The underlying genetic algorithm optimizes the parameters of the fuzzy sets associated with the individual nodes where they play a role of fuzzy "switches" by distributing a flow of processing completed within the tree. We discuss various forms of the fitness function that help capture the essence of the problem at hand (that could be either of classification nature when dealing with discrete outputs or regression-like when handling a continuous output variable). We quantify a nature of the generalization of the tree by studying an optimally adjusted spreads of the membership functions located at the nodes of the decision tree. A series of experiments exploiting synthetic and machine learning data is used to illustrate the performance of the G-DTs.