Enhancing Interval Type-2 Fuzzy Logic Systems: Learning for Precision and Prediction Intervals

In this paper, we tackle the task of generating Prediction Intervals (PIs) in high-risk scenarios by proposing enhancements for learning Interval Type-2 (IT2) Fuzzy Logic Systems (FLSs) to address their learning challenges. In this context, we first provide extra design flexibility to the Karnik-Mendel (KM) and Nie-Tan (NT) center of sets calculation methods to increase their flexibility for generating PIs. These enhancements increase the flexibility of KM in the defuzzification stage while the NT in the fuzzification stage. To address the large-scale learning challenge, we transform the IT2-FLS's constraint learning problem into an unconstrained form via parameterization tricks, enabling the direct application of deep learning optimizers. To address the curse of dimensionality issue, we expand the High-Dimensional Takagi-Sugeno-Kang (HTSK) method proposed for type-1 FLS to IT2-FLSs, resulting in the HTSK2 approach. Additionally, we introduce a framework to learn the enhanced IT2-FLS with a dual focus, aiming for high precision and PI generation. Through exhaustive statistical results, we reveal that HTSK2 effectively addresses the dimensionality challenge, while the enhanced KM and NT methods improved learning and enhanced uncertainty quantification performances of IT2-FLSs.