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.

翻译：一型和区间二型（IT2）模糊逻辑系统（FLS）凭借其简洁的基于规则的结构，在处理不确定性方面表现出色。然而，在学习大规模数据时会遇到挑战，例如维数灾难和FLS的训练复杂度。该复杂度主要源于定义模糊集的可学习参数需满足的约束条件，以及集合中心计算方法的复杂度，尤其是对于区间二型模糊逻辑系统。本文明确聚焦于FLS的学习问题，提出一种嵌入深度学习（DL）领域的计算高效学习方法。所提方法通过提供FLS的计算高效实现来应对其学习挑战，从而在利用深度学习框架提供的小批量优化器和自动微分机制的同时，最小化训练时间。我们在基准数据集上展示了DL框架在FLS中的高效性。