General Type-2 (GT2) Fuzzy Logic Systems (FLSs) are perfect candidates to quantify uncertainty, which is crucial for informed decisions in high-risk tasks, as they are powerful tools in representing uncertainty. In this paper, we travel back in time to provide a new look at GT2-FLSs by adopting Zadeh's (Z) GT2 Fuzzy Set (FS) definition, intending to learn GT2-FLSs that are capable of achieving reliable High-Quality Prediction Intervals (HQ-PI) alongside precision. By integrating Z-GT2-FS with the \(\alpha\)-plane representation, we show that the design flexibility of GT2-FLS is increased as it takes away the dependency of the secondary membership function from the primary membership function. After detailing the construction of Z-GT2-FLSs, we provide solutions to challenges while learning from high-dimensional data: the curse of dimensionality, and integrating Deep Learning (DL) optimizers. We develop a DL framework for learning dual-focused Z-GT2-FLSs with high performances. Our study includes statistical analyses, highlighting that the Z-GT2-FLS not only exhibits high-precision performance but also produces HQ-PIs in comparison to its GT2 and IT2 fuzzy counterparts which have more learnable parameters. The results show that the Z-GT2-FLS has a huge potential in uncertainty quantification.

翻译：通用二型模糊逻辑系统是量化不确定性的理想选择，这对于高风险任务中的知情决策至关重要，因其是表征不确定性的有力工具。本文回溯本源，采用Zadeh定义下的二型模糊集重新审视通用二型模糊逻辑系统，旨在学习既能保持精度又能生成可靠高质量预测区间的通用二型模糊逻辑系统。通过将Zadeh型二型模糊集与\(\alpha\)-平面表示相结合，我们证明了通用二型模糊逻辑系统的设计灵活性得以增强，因为该方法消除了次级隶属函数对主隶属函数的依赖性。在详细阐述Zadeh型通用二型模糊逻辑系统的构建后，我们针对高维数据学习中的两大挑战——维度灾难与深度学习优化器的集成——提出了解决方案。我们开发了一个深度学习框架，用于学习具有高性能的双目标Zadeh型通用二型模糊逻辑系统。研究包含统计分析，结果表明：与具有更多可学习参数的通用二型及区间二型模糊对应系统相比，Zadeh型通用二型模糊逻辑系统不仅展现出高精度性能，还能生成高质量预测区间。该结果揭示了Zadeh型通用二型模糊逻辑系统在不确定性量化方面的巨大潜力。