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.

翻译：本文针对高风险场景中生成预测区间的任务，通过提出增强型区间二型模糊逻辑系统的学习方法，解决其学习难题。首先，我们为Karnik-Mendel和Nie-Tan中心集合计算方法引入额外设计灵活性，以增强其生成预测区间的能力。这些增强方法分别提升了KM在解模糊阶段和NT在模糊化阶段的灵活性。为应对大规模学习挑战，我们通过参数化技巧将IT2-FLS的约束学习问题转化为无约束形式，从而直接应用深度学习优化器。针对维度灾难问题，我们将为一型FLS提出的高维Takagi-Sugeno-Kang方法扩展至IT2-FLS，提出HTSK2方法。此外，我们引入一个双目标学习框架，在保证高精度的同时实现预测区间生成。通过详尽的统计结果，我们揭示HTSK2有效应对维度挑战，且增强型KM和NT方法提升了IT2-FLS的学习性能与不确定性量化能力。