Efficient Learning of Fuzzy Logic Systems for Large-Scale Data Using Deep Learning

TL;DR

The paper tackles learning Type-1 and Interval Type-2 FLSs for large-scale data by embedding them in a DL framework that enables unconstrained optimization through parameterization. It introduces efficient, mini-batch capable inferences for both T1-FLS and IT2-FLS, including a GPU-friendly IT2 approach that eliminates the iterative Karnik–Mendel procedure by evaluating all binary combinations in parallel. The results show substantial training-time gains (up to $7218\times$ faster than KMA) while maintaining competitive RMSE across benchmark datasets, demonstrating scalable, uncertainty-aware FLSs in DL environments. These advances offer practical impact for deploying FLSs in large datasets and potentially in TinyML scenarios, with future work extending to PyTorch and TinyML integration.

Abstract

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.