Explainability and Efficiency in Fuzzy Logic Systems: Frameworks for Temporal Classification, Monotonicity, and Hybrid Predictive Modeling

This thesis advances fuzzy logic systems by improving explainability without compromising predictive accuracy in regression and time-series classification tasks. Motivated by the persistent trade-off between interpretability and performance in fuzzy methodologies, particularly in regulated domains requiring transparent decisions, the research develops novel frameworks addressing temporal modelling, semantic consistency, and hybrid inference. The work demonstrates that fuzzy systems can achieve semantic alignment with domain knowledge without compromising effectiveness. Key contributions include: The Optimized Time Series Interval Type-2 Fuzzy System framework introduces correlation-based time step selection with polynomial fitting for automated identification of predictive temporal patterns. This enables optimised fuzzy set generation over time periods, creating linguistic features (e.g., "recent" or "long-term") that enhance interpretability and noise robustness. Empirical evaluations on UCR classification benchmarks indicate clear advancements over baseline results, while providing explainable rules closely aligned with human temporal understanding. For semantic inconsistencies in fuzzy regression, the thesis formalises logical gaps, violations of monotonic relationships, and proposes a detection framework with quality metric guided rule insertion. Validated on a credit scoring dataset, this repair mechanism restores consistency via targeted interventions, preserving transparency with minimal impact on predictive accuracy and rule base size. In hybrid modelling, a novel Mamdani-TSK framework integrates linguistic consequents with constrained polynomials and dual weights optimised via ant colony algorithms. Benchmark results on KEEL datasets demonstrate RMSE improvements of up to 19\% over fuzzy baselines, achieving superior precision whilst maintaining full explainability. These innovations collectively extend fuzzy logic's theoretical foundations, offering reusable methodologies for explainable AI across classification and regression. The research provides empirical evidence from multiple domains, highlighting the practical value of these approaches in high-stakes applications. This work reinforces fuzzy logic's role in responsible AI, showing that enhanced explainability through systematic innovations can yield trustworthy systems in an increasingly regulated world.