arXiv:2504.18636v2 Announce Type: replace Abstract: Phishing attacks represent an increasingly sophisticated and pervasive threat to individuals and organizations, causing significant financial losses, identity theft, and severe damage to institutional reputations. Existing phishing detection methods often struggle to simultaneously achieve high accuracy and explainability, either failing to detect novel attacks or operating as opaque black-box models. To address this critical gap, we propose a novel phishing URL detection system based on a first-order Takagi-Sugeno-Kang (TSK) fuzzy inference model optimized through gradient-based techniques. Our approach intelligently combines the interpretability and human-like reasoning capabilities of fuzzy logic with the precision and adaptability provided by gradient optimization methods, specifically leveraging the Adam optimizer for efficient parameter tuning. Experiments conducted using a comprehensive dataset of over 235,000 URLs demonstrate rapid convergence, exceptional predictive performance (accuracy averaging 99.95% across 5 cross-validation folds, with a perfect AUC i.e. 1.00). Furthermore, optimized fuzzy rules and membership functions improve interoperability, clearly indicating how the model makes decisions - an essential feature for cybersecurity applications. This high-performance, transparent, and interpretable phishing detection framework significantly advances current cybersecurity defenses, providing practitioners with accurate and explainable decision-making tools.