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.

通过改进 Interval Type-2 Fuzzy Logic Systems (FLSs) 来提高高风险场景下的预测区间 (Prediction Intervals) 生成，包括增加 Karnik-Mendel (KM) 和 Nie-Tan (NT) 方法的灵活性、通过参数化技巧解决大规模学习挑战、对抗维度灾难问题，以及引入高维 Takagi-Sugeno-Kang 方法来增强不确定性量化和提高学习性能。