Synthetic feature extraction and synergy detection for fuzzy set-based decision tree optimization

This thesis sets out from the limitations of modeling the uncertain and multi-layered structure of the real world using two-valued classical logic; it addresses fuzzy set theory and its extensions, which aim to overcome these limitations, from both theoretical and applied perspectives. While establishing the theoretical foundation, the basic building blocks of fuzzy sets—such as membership functions, α-cuts, support, and core concepts—are first defined. Subsequently, interval-valued, intuitionistic, Pythagorean, Type-2, hesitant, and multi-fuzzy sets are examined comparatively. The study endeavors to demonstrate how each of these generalizations handles uncertainty differently and in which types of problems they excel. In the applied section of the study, the ID3, C4.5, and Fuzzy ID3 algorithms are examined, highlighting the differences among them. Building upon this foundation, a novel algorithm is proposed that integrates synthetic feature generation based on Kendall tau_b correlation, dynamic direction alignment, and elite pool filtering. The algorithm is tested on both a controlled dataset and scan data compiled from the literature; concrete findings are used to discuss when synthetic features are beneficial and when individual features are sufficient. Ultimately, this thesis is the product of an effort to apply fuzzy set theory—often remaining an abstract concept—to classification problems, aiming to produce models that are both more accurate and interpretable by domain experts.