Odyssey of Interval Type-2 Fuzzy Logic Systems: Learning Strategies for Uncertainty Quantification

This study presents an Odyssey of enhancements for interval type-2 (IT2) fuzzy logic systems (FLSs) for efficient learning in the pursuit of generating prediction intervals (PIs) for high-risk scenarios. We start by presenting enhancements to Karnik-Mendel (KM) and Nie-Tan (NT) center of sets calculation methods (CSCMs) to increase their learning capacities. The enhancements increase the flexibility of KM in the defuzzification stage while the NT in the fuzzification stage. We also present a parametric KM CSCM, aimed to reduce the inference complexity of KM while providing flexibility. To address large-scale learning challenges, we convert the constraint learning problem of IT2-FLS into an unconstrained form using parameterization tricks, allowing for the direct application of deep learning optimizers and automatic differentiation methods. In tackling the curse of dimensionality issue, we expand the high-dimensional Takagi-Sugeno-Kang method (HTSK) proposed for type-1 FLS to IT2-FLSs, resulting in the HTSK for IT2-FLSs. We also introduce an enhanced HTSK for IT2-FLSs from an alternative perspective, featuring a comparatively simpler computational nature. Finally, we introduce a framework to learn IT2-FLSs with a dual focus, aiming for high precision and PI generation. Our comprehensive statistical analysis demonstrates the effectiveness of the enhancements for uncertainty quantification via IT2-FLSs.