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。

增强间隔型 - 2 模糊逻辑系统：精度和预测区间的学习

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

Type-1 and Interval Type-2 (IT2) Fuzzy Logic Systems (FLS) excel in handling
uncertainty alongside their parsimonious rule-based structure. Yet, in learning
large-scale data challenges arise, such as the curse of dimensionality and
training complexity of FLSs. The complexity is due mainly to the constraints to
be satisfied as the learnable parameters define FSs and the complexity of the
center of the sets calculation method, especially of IT2-FLSs. This paper
explicitly focuses on the learning problem of FLSs and presents a
computationally efficient learning method embedded within the realm of Deep
Learning (DL). The proposed method tackles the learning challenges of FLSs by
presenting computationally efficient implementations of FLSs, thereby
minimizing training time while leveraging mini-batched DL optimizers and
automatic differentiation provided within the DL frameworks. We illustrate the
efficiency of the DL framework for FLSs on benchmark datasets.

本文提出了一种嵌入到深度学习领域的计算高效的模糊逻辑系统（FLS）学习方法，通过提供计算高效的 FLS 实现，最小化训练时间并利用深度学习框架中提供的小批量优化器和自动微分机制，解决了 FLS 学习的挑战，并在基准数据集上展示了深度学习框架在 FLS 中的高效性。